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[1{/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map}] [2] [3] [4] Overfull \hbox (6.14793pt too wide) in paragraph at lines 605--608 \T1/lmr/m/n/10.95 San-dic ge-tippt. Bei An-mer-kun-gen be-zie-hungs-wei-se beim Auf-fin-den von Feh-lern schickt (/usr/share/texmf/tex/latex/lm/t1lmtt.fd) [5] [6] Kapitel 1. Class scrbook Warning: \float@addtolists detected! (scrbook) Implementation of \float@addtolist became (scrbook) deprecated in KOMA-Script v3.01 2008/11/14 and (scrbook) has been replaced by more several more flexible (scrbook) features of package `tocbasic`. (scrbook) Since Version 3.12 support for deprecated (scrbook) \float@addtolist interface has been (scrbook) restricted to only some of the KOMA-Script (scrbook) features and been removed from others. (scrbook) Loading of package `scrhack' may help to (scrbook) avoid this warning, if you are using a (scrbook) a package that still implements the (scrbook) deprecated \float@addtolist interface . Underfull \hbox (badness 10000) in paragraph at lines 677--678 Underfull \hbox (badness 10000) in paragraph at lines 679--680 Underfull \hbox (badness 10000) in paragraph at lines 681--682 Underfull \vbox (badness 7168) has occurred while \output is active [7] Overfull \hbox (19.46976pt too wide) in paragraph at lines 718--719 []\T1/lmr/m/it/10.95 Eine []\T1/lmr/bx/it/10.95 dif-fe-ren-zier-ba-re Man- Underfull \hbox (badness 10000) in paragraph at lines 718--719 Underfull \hbox (badness 10000) in paragraph at lines 766--767 [8] Overfull \hbox (0.8859pt too wide) in paragraph at lines 781--781 [] Overfull \hbox (6.45883pt too wide) in paragraph at lines 794--797 []\T1/lmr/m/it/10.95 Eine ste-ti-ge Ab-bil-dung $\OML/lmm/m/it/10.95 f [] [] M \OMS/lmsy/m/n/10.95 ! 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[15] Underfull \hbox (badness 10000) in paragraph at lines 1332--1334 Overfull \hbox (2.66713pt too wide) in paragraph at lines 1387--1387 [] [16] [17] [18] Kapitel 3. [19] Overfull \hbox (14.65828pt too wide) in paragraph at lines 1626--1626 [] [20] LaTeX Warning: Reference `satz-3-4' on page 21 undefined on input line 1730. [21] LaTeX Warning: Reference `satz-3-4' on page 22 undefined on input line 1738. LaTeX Warning: Reference `satz-3-4' on page 22 undefined on input line 1777. [22] [23] [24] Kapitel 4. LaTeX Warning: Reference `satz-2-9' on page 25 undefined on input line 1928. Overfull \hbox (3.13892pt too wide) in paragraph at lines 1956--1957 []\T1/lmr/m/n/10.95 Ist $\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 '; U\OT1/lmr/m /n/10.95 )$ \T1/lmr/m/n/10.95 ei-ne Kar-te von $\OML/lmm/m/it/10.95 M$\T1/lmr/m /n/10.95 , so sind die Ab-bil-dun-gen $\OML/lmm/m/it/10.95 U \OMS/lmsy/m/n/10.9 5 ! [] \OML/lmm/m/it/10.95 M\OMS/lmsy/m/n/10.95 j[]\OML/lmm/m/it/10.95 ; p \OM S/lmsy/m/n/10.95 7! [25] Overfull \hbox (17.45334pt too wide) in paragraph at lines 2009--2010 []\T1/lmr/m/it/10.95 Die Lie-klam-mer ist ei-ne schief-sym-me-tri-sche $[]$-bil ineare Ab-bil-dung $\OMS/lmsy/m/n/10.95 V\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.9 5 M\OT1/lmr/m/n/10.95 ) \OMS/lmsy/m/n/10.95 ^^B [26] Overfull \hbox (12.142pt too wide) in paragraph at lines 2049--2049 [] [27] LaTeX Warning: Citation `lang1995differential' on page 28 undefined on input li ne 2112. LaTeX Warning: Reference `satz-4-6' on page 28 undefined on input line 2126. LaTeX Warning: Reference `satz-4-6-ii' on page 28 undefined on input line 2126. [28] LaTeX Warning: Reference `satz-4-9' on page 29 undefined on input line 2186. (/usr/share/texmf/tex/latex/lm/omslmr.fd) Overfull \hbox (8.91791pt too wide) in paragraph at lines 2203--2203 [] Overfull \hbox (33.22739pt too wide) in paragraph at lines 2223--2224 []\T1/lmr/m/it/10.95 Ein Vek-tor-feld auf $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/it/ 10.95 hei^^Dst []\T1/lmr/bx/it/10.95 voll[]-stän[]-dig\T1/lmr/m/it/10.95 , LaTeX Warning: Reference `korollar-4-7' on page 29 undefined on input line 2238 . LaTeX Warning: Reference `korollar-4-8' on page 29 undefined on input line 2240 . [29] Overfull \hbox (3.79543pt too wide) in paragraph at lines 2257--2258 []\T1/lmr/m/n/10.95 Integralkurven exis-tie-ren für al- Overfull \hbox (7.98071pt too wide) in paragraph at lines 2277--2277 [] [30] [31] [32] Kapitel 5. [33] Overfull \hbox (28.94324pt too wide) in paragraph at lines 2492--2495 []\T1/lmr/m/n/10.95 Die Vek-tor-bün-del $\OML/lmm/m/it/10.95 E; E[]$ \T1/lmr/m/ n/10.95 über $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/n/10.95 hei^^Dsen []\T1/lmr/bx/n /10.95 iso-morph\T1/lmr/m/n/10.95 , wenn ein $\OML/lmm/m/it/10.95 M$\T1/lmr/m/n /10.95 -Vektor[]-bündel[]-morphismus Overfull \hbox (12.94687pt too wide) in paragraph at lines 2537--2538 []\T1/lmr/m/it/10.95 Es sei $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/it/10.95 ei-ne gl at-te Man-nig-fal-tig-keit mit ei-ner of-fe-nen Über-de-ckung $\OMS/lmsy/m/n/10 .95 f\OML/lmm/m/it/10.95 U[]\OMS/lmsy/m/n/10.95 g[]$ [34] [35] [36] Overfull \hbox (3.51917pt too wide) in paragraph at lines 2664--2666 \T1/lmr/m/n/10.95 ein Ele-ment $\OML/lmm/m/it/10.95 ' \OMS/lmsy/m/n/10.95 \OML/lmm/m/it/10.95 \OMS/lmsy/m/n/10.95 2 []\OT1/lmr/m/n/10.95 (\OML/lmm/m/i t/10.95 V[] \OMS/lmsy/m/n/10.95 \OML/lmm/m/it/10.95 V[]; W[] \OMS/lmsy/m/n/10.95 \OML/lmm/m/it/10.95 W[]\OT1/lmr/m/n/10.95 )$\T1/lmr/m/n/10.95 . Sind $\OML/lmm /m/it/10.95 V$\T1/lmr/m/n/10.95 , $\OML/lmm/m/it/10.95 W$ \T1/lmr/m/n/10.95 Vek -tor-räu-me und $\OML/lmm/m/it/10.95 '[]; [] ; '[] \OMS/lmsy/m/n/10.95 2 LaTeX Warning: Reference `satz-5-2' on page 37 undefined on input line 2680. LaTeX Warning: Reference `satz-5-2' on page 37 undefined on input line 2685. [37] [38] Overfull \hbox (4.49565pt too wide) in paragraph at lines 2755--2758 \OML/lmm/m/it/10.95 M$\T1/lmr/m/n/10.95 ; $\OMS/lmsy/m/n/10.95 T[]\OT1/lmr/m/n/ 10.95 (\OML/lmm/m/it/10.95 M\OT1/lmr/m/n/10.95 ) = \OMS/lmsy/m/n/10.95 V\OT1/lm r/m/n/10.95 (\OML/lmm/m/it/10.95 M\OT1/lmr/m/n/10.95 )$\T1/lmr/m/n/10.95 . Es b e-zeich-ne $\OMS/lmsy/m/n/10.95 V[]\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 M\OT 1/lmr/m/n/10.95 ) = \OMS/lmsy/m/n/10.95 T[]\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10 .95 M\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/10.95 den Raum der $\OT1/lmr/m/n/10.95 ( 0\OML/lmm/m/it/10.95 ; \OT1/lmr/m/n/10.95 1)$\T1/lmr/m/n/10.95 -Tensorfelder. (/usr/share/texlive/texmf-dist/tex/latex/ucs/data/uni-0.def) LaTeX Warning: Reference `exc:ueb5-a1' on page 39 undefined on input line 2769. LaTeX Warning: Reference `satz-2-10' on page 39 undefined on input line 2796. [39] [40] Package hyperref Warning: Composite letter `\textasciidieresis+s' (hyperref) not defined in PD1 encoding, (hyperref) removing `\textasciidieresis' on input line 2883. [41] LaTeX Warning: Reference `prop-5-4' on page 42 undefined on input line 2910. LaTeX Warning: Reference `def-5-5' on page 42 undefined on input line 2944. [42] [43] [44] LaTeX Warning: Reference `lemma-5-9' on page 45 undefined on input line 3081. LaTeX Warning: Reference `lemma-5-9-iv' on page 45 undefined on input line 3081 . Overfull \hbox (34.08974pt too wide) in paragraph at lines 3081--3082 []\T1/lmr/m/n/10.95 Der Quo-ti-ent $\OML/lmm/m/it/10.95 H[]\OT1/lmr/m/n/10.95 ( \OML/lmm/m/it/10.95 M\OT1/lmr/m/n/10.95 ) = []$ \T1/lmr/m/n/10.95 hei^^Dst die $\OML/lmm/m/it/10.95 k$\T1/lmr/m/n/10.95 -te []\T1/lmr/bx/n/10.95 deRahm-Ko[]-h omologie[]-gruppe\T1/lmr/m/n/10.95 . [45] [46] Kapitel 6. Underfull \vbox (badness 5316) has occurred while \output is active [47] [48] [49] LaTeX Warning: Citation `boothby1986introduction' on page 50 undefined on input line 3321. LaTeX Warning: Reference `Satz-6-3' on page 50 undefined on input line 3323. Overfull \hbox (28.74033pt too wide) in paragraph at lines 3323--3325 []\T1/lmr/m/n/10.95 (von Satz []) Es sei $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/n/10 .95 ei-ne glat-te, $\OML/lmm/m/it/10.95 m$\T1/lmr/m/n/10.95 -dimensionale Man-n ig-fal-tig-keit. $\OMS/lmsy/m/n/10.95 f\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 '[]; U[]\OT1/lmr/m/n/10.95 )\OMS/lmsy/m/n/10.95 g[]$ [50] Overfull \hbox (1.8736pt too wide) in paragraph at lines 3365--3365 [] [51] [52] LaTeX Warning: Reference `lemma-6-9' on page 53 undefined on input line 3497. Overfull \hbox (6.56665pt too wide) in paragraph at lines 3496--3498 []\T1/lmr/m/n/10.95 Es sei $\OML/lmm/m/it/10.95 ^^M$ \T1/lmr/m/n/10.95 mi-ni-ma -le Geo-dä-ti-sche, das hei^^Dst $\OMS/lmsy/m/n/10.95 L\OT1/lmr/m/n/10.95 (\OML /lmm/m/it/10.95 ^^M\OMS/lmsy/m/n/10.95 j[]\OT1/lmr/m/n/10.95 ) = \OML/lmm/m/it/ 10.95 ^^Ut \OT1/lmr/m/n/10.95 = d(\OML/lmm/m/it/10.95 ^^M\OT1/lmr/m/n/10.95 (0) \OML/lmm/m/it/10.95 ; ^^M\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 t\OT1/lmr/m/n/ 10.95 ))$\T1/lmr/m/n/10.95 . [53] [54] Kapitel 7. [55] (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/ueuf.fd) [56] [57] LaTeX Warning: Reference `kapitel-5' on page 58 undefined on input line 3725. LaTeX Warning: Reference `eqn:omega-tilde' on page 58 undefined on input line 3 729. [58] [59] [60] LaTeX Warning: Reference `prop-7-9' on page 61 undefined on input line 3882. Overfull \hbox (2.81465pt too wide) in paragraph at lines 3881--3883 \T1/lmr/m/it/10.95 wobei $\OML/lmm/m/it/10.95 S[]$ \T1/lmr/m/it/10.95 den nach Pro-po-si-ti-on [] ein-deu-ti-gen par-al-le-len Schnitt ent-lang $\OML/lmm/m/it /10.95 c$ \T1/lmr/m/it/10.95 mit $\OML/lmm/m/it/10.95 S[]\OT1/lmr/m/n/10.95 (\O ML/lmm/m/it/10.95 s\OT1/lmr/m/n/10.95 ) = [61] Overfull \hbox (2.34628pt too wide) in paragraph at lines 3972--3973 []\T1/lmr/m/it/10.95 Auf ei-ner Rie-mann-schen Man-nig-fal-tig-keit exis-tiert Overfull \hbox (9.88931pt too wide) in paragraph at lines 3984--3984 [] [62] LaTeX Warning: Reference `satz-7-12' on page 63 undefined on input line 4005. Overfull \hbox (13.34167pt too wide) in paragraph at lines 4020--4020 [] [63] Overfull \hbox (1.11209pt too wide) in paragraph at lines 4057--4059 []\T1/lmr/bx/n/10.95 Lokale Ko-or-di-na-ten[] \T1/lmr/m/n/10.95 Es sei $\OT1/l mr/m/n/10.95 (\OML/lmm/m/it/10.95 M; g\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/10.95 e i-ne Riem-mann-sche Man-nig-fal-tig-keit mit Levi- Overfull \hbox (4.19382pt too wide) in paragraph at lines 4085--4087 \T1/lmr/m/n/10.95 (Formale Pro-dukt-re-gel: $\OMS/lmsy/m/n/10.95 r[]\OT1/lmr/m/ n/10.95 (\OMS/lmsy/m/n/10.95 r[]\OML/lmm/m/it/10.95 Z\OT1/lmr/m/n/10.95 ) = \OM S/lmsy/m/n/10.95 r[]\OT1/lmr/m/n/10.95 (\OMS/lmsy/m/n/10.95 r\OML/lmm/m/it/10.9 5 Z\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 Y\OT1/lmr/m/n/10.95 )) = (\OMS/lmsy/ m/n/10.95 r[]\OT1/lmr/m/n/10.95 (\OMS/lmsy/m/n/10.95 r\OML/lmm/m/it/10.95 Z\OT1 /lmr/m/n/10.95 ))(\OML/lmm/m/it/10.95 Y\OT1/lmr/m/n/10.95 ) + (\OMS/lmsy/m/n/10 .95 r\OML/lmm/m/it/10.95 Z\OT1/lmr/m/n/10.95 )(\OMS/lmsy/m/n/10.95 r[]\OML/lmm/ m/it/10.95 Y\OT1/lmr/m/n/10.95 ) = [64] [65] [66] Kapitel 8. [67] LaTeX Warning: Reference `satz-4-9' on page 68 undefined on input line 4284. [68] Overfull \hbox (1.50125pt too wide) in paragraph at lines 4316--4318 []\T1/lmr/m/n/10.95 Der De-fi-ni-ti-ons-be-reich $\OMS/lmsy/m/n/10.95 D[]$ \T1/ lmr/m/n/10.95 des geo-dä-ti-schen Flus-ses ist ei-ne of-fe-ne Men-ge in $[] \OM S/lmsy/m/n/10.95 ^^B [][] \OML/lmm/m/it/10.95 M$ LaTeX Warning: Reference `satz-4-6' on page 69 undefined on input line 4330. [69] Underfull \vbox (badness 6396) has occurred while \output is active [70] LaTeX Warning: Reference `dfn-8-1' on page 71 undefined on input line 4487. Overfull \hbox (15.84973pt too wide) in paragraph at lines 4529--4529 [] [71] [72] LaTeX Warning: Reference `satz-8-7' on page 73 undefined on input line 4588. LaTeX Warning: Reference `dfn-8-1' on page 73 undefined on input line 4599. Overfull \hbox (3.42616pt too wide) in paragraph at lines 4612--4612 [] LaTeX Warning: Reference `kor-8-8' on page 73 undefined on input line 4613. LaTeX Warning: Reference `kor-8-8' on page 73 undefined on input line 4628. [73] LaTeX Warning: Reference `satz-8-7' on page 74 undefined on input line 4667. LaTeX Warning: Reference `satz-8-7' on page 74 undefined on input line 4691. LaTeX Warning: Reference `kor-8-9' on page 74 undefined on input line 4697. [74] LaTeX Warning: Reference `kor-8-8' on page 75 undefined on input line 4735. LaTeX Warning: Reference `kor-8-9' on page 75 undefined on input line 4792. [75] LaTeX Warning: Reference `satz-8-7' on page 76 undefined on input line 4845. [76] Kapitel 9. [77] LaTeX Warning: Reference `prop-7-3' on page 78 undefined on input line 4963. [78] Underfull \vbox (badness 5008) has occurred while \output is active [79] LaTeX Warning: Citation `milnor1963morsetheo' on page 80 undefined on input lin e 5116. [80] [81] LaTeX Warning: Reference `eqn:jacobifeld-dgl' on page 82 undefined on input lin e 5226. LaTeX Warning: Reference `eqn:jacobifeld-dgl' on page 82 undefined on input lin e 5243. [82] [83] LaTeX Warning: Reference `thm:lemma-9-4' on page 84 undefined on input line 533 6. LaTeX Warning: Reference `thm:kor-8-12' on page 84 undefined on input line 5339 . LaTeX Warning: Reference `thm:kor-8-12-iii' on page 84 undefined on input line 5339. LaTeX Warning: Reference `satz-9-5' on page 84 undefined on input line 5410. [84] [85] LaTeX Warning: Reference `satz-9-8' on page 86 undefined on input line 5505. [86] LaTeX Warning: Reference `thm:lemma-9-10' on page 87 undefined on input line 55 49. LaTeX Warning: Reference `thm:lemma-9-4' on page 87 undefined on input line 558 9. [87] [88] LaTeX Warning: Command \d invalid in math mode on input line 5695. [89] LaTeX Warning: Citation `Cheng1975' on page 90 undefined on input line 5750. [90] LaTeX Warning: Reference `hopf-rinow' on page 91 undefined on input line 5791. LaTeX Warning: Reference `prop-9-12' on page 91 undefined on input line 5822. LaTeX Warning: Citation `kobayashi-nomizu1963foundations-diffgeo' on page 91 un defined on input line 5836. [91] [92] [93] Overfull \hbox (7.75755pt too wide) in paragraph at lines 6079--6081 []\T1/lmr/m/it/10.95 Es sei $\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 M; g\OT1/l mr/m/n/10.95 )$ \T1/lmr/m/it/10.95 ei-ne voll-stän-di-ge Rie-mann-sche Man- LaTeX Warning: Reference `prop-9-12' on page 94 undefined on input line 6097. LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. [94] Overfull \hbox (13.20297pt too wide) in paragraph at lines 6137--6137 [] [95] [96] [97] [98] LaTeX Warning: Reference `thm:lemma-9-16' on page 99 undefined on input line 63 80. [99] LaTeX Warning: Citation `Cheng1975' on page 100 undefined on input line 6486. [100] LaTeX Warning: Reference `thm:satz-alexandrov-toponogov' on page 101 undefined on input line 6585. [101] LaTeX Warning: Citation `Cheng1975' on page 102 undefined on input line 6642. [102] [103] [104] [105] [106] Anhang A. Overfull \hbox (6.49251pt too wide) in paragraph at lines 6959--6959 [] Overfull \hbox (33.98529pt too wide) in paragraph at lines 6979--6981 $\OML/lmm/m/it/10.95 V$ \T1/lmr/m/n/10.95 ist of-fen in $\OT1/lmr/m/n/10.95 ([] [])[]$\T1/lmr/m/n/10.95 : $\OML/lmm/m/it/10.95 V \OT1/lmr/m/n/10.95 = [][]([][] \OMS/lmsy/m/n/10.95 nf\OT1/lmr/m/n/10.95 0\OMS/lmsy/m/n/10.95 g\OT1/lmr/m/n/10 .95 )$ \T1/lmr/m/n/10.95 mit $[]\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 v[]; [] ; v[]\OT1/lmr/m/n/10.95 ) = ([](\OML/lmm/m/it/10.95 k \OMS/lmsy/m/n/10.95 ^^B \OML/lmm/m/it/10.95 k[]\OT1/lmr/m/n/10.95 ))$ [107] Overfull \hbox (30.97409pt too wide) in paragraph at lines 6992--6993 []\T1/lmr/m/n/10.95 Für $\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 v[]; [] ; v[]\ OT1/lmr/m/n/10.95 ) \OMS/lmsy/m/n/10.95 2 \OML/lmm/m/it/10.95 ^^Y[]\OT1/lmr/m/n /10.95 (\OML/lmm/m/it/10.95 U[]\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/10.95 ist $\OM L/lmm/m/it/10.95 B \OMS/lmsy/m/n/10.95 ^^N \OML/lmm/m/it/10.95 ^^Y\OT1/lmr/m/n/ 10.95 (\OML/lmm/m/it/10.95 v[]; [] ; v[]\OT1/lmr/m/n/10.95 ) = (([][] \OMS/lmsy /m/n/10.95 j[]\OT1/lmr/m/n/10.95 )[]\OML/lmm/m/it/10.95 X[]\OT1/lmr/m/n/10.95 ) []$\T1/lmr/m/n/10.95 . Overfull \hbox (11.24615pt too wide) in paragraph at lines 6992--6993 \T1/lmr/m/n/10.95 Die Dar-stel-lungs-ma-trix von $\OT1/lmr/m/n/10.95 ([][] \OMS /lmsy/m/n/10.95 j[]\OT1/lmr/m/n/10.95 )[]$ \T1/lmr/m/n/10.95 be-züg-lich $\OMS/ lmsy/m/n/10.95 f\OML/lmm/m/it/10.95 x[]\OMS/lmsy/m/n/10.95 g\OML/lmm/m/it/10.95 ; \OMS/lmsy/m/n/10.95 f\OML/lmm/m/it/10.95 y[]\OMS/lmsy/m/n/10.95 g$ \T1/lmr/m /n/10.95 hängt [108] Overfull \hbox (38.54076pt too wide) in paragraph at lines 7103--7104 []$\OML/lmm/m/it/10.95 '; $ \T1/lmr/m/n/10.95 Ho-möo-mor-phis-men, $\OT1/lmr/m /n/10.95 ^^H : \OMS/lmsy/m/n/10.95 f\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 x[] ; [] ; x[]\OT1/lmr/m/n/10.95 ) \OMS/lmsy/m/n/10.95 2 [][] j \OML/lmm/m/it/10.95 x[] < \OT1/lmr/m/n/10.95 1\OMS/lmsy/m/n/10.95 g ! [][]\OML/lmm/m/it/10.95 ; x \OMS/lmsy/m/n/10.95 7! []\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 x[]; [] ; x[]\ OT1/lmr/m/n/10.95 ) \OMS/lmsy/m/n/10.95 ) [109] Overfull \hbox (10.38538pt too wide) in paragraph at lines 7171--7171 [] [110]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7251 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7257 \begin{Aufg} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b] [111]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7272 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.4}) has been already used, duplicate ignored \relax l.7278 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.7282 \begin{Loes} [112]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.7324 \begin{Loes} \begin{enumerate}[label=\alph*),widest=b,leftmargin=*] [113]pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.7378 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.4}) has been already used, duplicate ignored \relax l.7419 \begin{Loes} [114]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7447 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7458 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7473 \begin{Aufg} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b] [115]pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.7480 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.2}) has been already used, duplicate ignored \relax l.7518 \begin{Loes} \begin{enumerate}[label=\alph*),leftmargin=*,widest=a] [116]pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.7550 \begin{Loes} \begin{enumerate}[label=\alph*),widest=a,leftmargin=*] [117]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7589 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7600 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7610 \begin{Aufg} [118]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.4}) has been already used, duplicate ignored \relax l.7616 \begin{Aufg} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b]pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been a lready used, duplicate ignored \relax l.7625 \begin{Loes} [119]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.7664 \begin{Loes} Overfull \hbox (39.6498pt too wide) in paragraph at lines 7679--7679 [][] [120]pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.7721 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.4}) has been already used, duplicate ignored \relax l.7751 \begin{Loes} \begin{enumerate}[label=(\alph*),leftmargin=*,widest=a] [121]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7783 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7788 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7801 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.7811 \begin{Loes} \label{exc:ueb5-a1} [122] [123] Overfull \hbox (30.3387pt too wide) in paragraph at lines 7867--7868 []\T1/lmr/m/n/10.95 lokale Ko-or-di-na-ten $\U/msa/m/n/10.95 []\OML/lmm/m/it/ 10.95 x[]$\T1/lmr/m/n/10.95 , Ko-ef-fi-zi-en-ten von $\OML/lmm/m/it/10.95 ![]; [] ; X[]$ pdfTeX warning (ext4): destination with the same identifier (name{Loes.2}) has been already used, duplicate ignored \relax l.7895 \begin{Loes} \begin{enumerate}[label=\alph*), leftmargin=*] [124]pdfTeX w arning (ext4): destination with the same identifier (name{Loes.3}) has been alr eady used, duplicate ignored \relax l.7910 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7935 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7946 \begin{Aufg} Overfull \hbox (8.36499pt too wide) in paragraph at lines 7953--7954 []\T1/lmr/m/n/10.95 Die Rie-mann-sche Man-nig-fal-tig-keit $\OT1/lmr/m/n/10.95 (\U/msb/m/n/10.95 H[]\OML/lmm/m/it/10.95 ; g\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/1 0.95 heiÿt $\OML/lmm/m/it/10.95 n$\T1/lmr/m/it/10.95 -dimensionaler hy-per-bo-l i-scher Raum\T1/lmr/m/n/10.95 . pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7956 \begin{Aufg} [125]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.1}) has been already used, duplicate ignored \relax l.7967 \begin{Loes} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b]pdfTeX warning (ext4): destination with the same identifier (name{Loes.2}) has been a lready used, duplicate ignored \relax l.7974 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.7978 \begin{Loes} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been a lready used, duplicate ignored \relax l.7996 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8002 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.8012 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.8024 \begin{Loes} [126]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.8052 \begin{Loes} [127] [128] Overfull \hbox (6.37263pt too wide) in paragraph at lines 8109--8111 []$\OMS/lmsy/m/n/10.95 r[]$ \T1/lmr/m/n/10.95 ist der []\T1/lmr/bx/n/10.95 Levi -Civita Zu-sam-men-hang \T1/lmr/m/n/10.95 von $\OT1/lmr/m/n/10.95 (\OML/lmm/m/i t/10.95 M; g\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/10.95 mit $\OML/lmm/m/it/10.95 g\ OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 X; Y\OT1/lmr/m/n/10.95 ) = pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.8115 \begin{Loes} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been a lready used, duplicate ignored \relax l.8153 \begin{Aufg} [129]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8163 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.8175 \begin{Aufg} Overfull \hbox (35.37292pt too wide) in paragraph at lines 8207--8207 [] Underfull \vbox (badness 10000) has occurred while \output is active [130]pdfTe X warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.8211 \begin{Loes} [131]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.8241 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.8277 \begin{Loes} [132]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.8297 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8303 \begin{Aufg} Overfull \hbox (18.51144pt too wide) in paragraph at lines 8304--8305 []\T1/lmr/m/n/10.95 Bestimmen Sie die Schnitt-krüm-mun-gen der Rie-mann-schen M an-nig-fal-tig-kei-ten $\OT1/lmr/m/n/10.95 ([][]\OML/lmm/m/it/10.95 ; 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[134] Overfull \hbox (19.2354pt too wide) in paragraph at lines 8401--8402 []\T1/lmr/m/n/10.95 Wir be-rech-nen die Kom-po-nen-ten $\OML/lmm/m/it/10.95 R[] \OT1/lmr/m/n/10.95 = \OML/lmm/m/it/10.95 R\OT1/lmr/m/n/10.95 ([]\OML/lmm/m/it/ 10.95 ; []; []; []\OT1/lmr/m/n/10.95 ) = \OML/lmm/m/it/10.95 g\OT1/lmr/m/n/10.9 5 (\OML/lmm/m/it/10.95 R\OT1/lmr/m/n/10.95 ([]\OML/lmm/m/it/10.95 ; []\OT1/lmr/ m/n/10.95 )[]\OML/lmm/m/it/10.95 ; []\OT1/lmr/m/n/10.95 )$ Overfull \hbox (13.04242pt too wide) in paragraph at lines 8411--8411 [] Overfull \hbox (36.99953pt too wide) in paragraph at lines 8420--8420 [] Underfull \vbox (badness 1755) has occurred while \output is active [135] Overfull \hbox (100.82646pt too wide) in paragraph at lines 8442--8442 [] Overfull \hbox (26.51044pt too wide) in paragraph at lines 8457--8457 [] [136]pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.8462 \begin{Loes} Overfull \hbox (26.24988pt too wide) in paragraph at lines 8492--8492 [] Underfull \vbox (badness 10000) has occurred while \output is active [137] [138] [139] [140] [141]pdfTeX warning (ext4): destination with the same identif ier (name{Aufg.1}) has been already used, duplicate ignored \relax l.8719 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8730 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.8736 \begin{Loes} [142]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.8776 \begin{Loes} \begin{description}[leftmargin=*] LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . [143] [144]pdfTeX warning (ext4): destination with the same identifier (name{Au fg.1}) has been already used, duplicate ignored \relax l.8901 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8909 \begin{Aufg} [145]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.1}) has been already used, duplicate ignored \relax l.8934 \begin{Loes} [146]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.8987 \begin{Loes} [147]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.9083 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.9091 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.9095 \begin{Aufg} [148]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.1}) has been already used, duplicate ignored \relax l.9099 \begin{Loes} \begin{description}[leftmargin=*] LaTeX Warning: Citation `olum' on page 149 undefined on input line 9150. [149] LaTeX Warning: Citation `brody1960' on page 150 undefined on input line 9152. pdfTeX warning (ext4): destination with the same identifier (name{Loes.2}) has been already used, duplicate ignored \relax l.9156 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.9161 \begin{Loes} Overfull \hbox (0.37314pt too wide) in paragraph at lines 9181--9181 [] Overfull \hbox (0.37314pt too wide) in paragraph at lines 9207--9207 [] No file DiffGeo2012Skript.ind. No file DiffGeo2012Skript.gls. No file DiffGeo2012Skript.bbl. [150] (./DiffGeo2012Skript.aux) Package rerunfilecheck Warning: File `DiffGeo2012Skript.out' has changed. (rerunfilecheck) Rerun to get outlines right (rerunfilecheck) or use package `bookmark'. LaTeX Font Warning: Some font shapes were not available, defaults substituted. LaTeX Warning: There were undefined references. LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right. ) (see the transcript file for additional information)pdfTeX warning (dest): name {glo:spur} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Dualraum} has been referenced but does not exis t, replaced by a fixed one pdfTeX warning (dest): name{glo:GL} has been referenced but does not exist, rep laced by a fixed one pdfTeX warning (dest): name{glo:Homomorphismus} has been referenced but does no t exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Isomorphismus} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{glo:supp} has been referenced but does not exist, r eplaced by a fixed one pdfTeX warning (dest): name{glo:Kurve} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Produkttopologie} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Endomorphismus} has been referenced but does no t exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Diffeomorphismus} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Homoeomorphismus} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Topologie} has been referenced but does not exi st, replaced by a fixed one pdfTeX warning (dest): name{glo:Hausdorff-Raum} has been referenced but does no t exist, replaced by a fixed one {/usr/share/texmf/fonts/enc/dvips/lm/lm-rm.enc}{/usr/share/texmf/fonts/enc/dvip s/lm/lm-mathsy.enc}{/usr/share/texmf/fonts/enc/dvips/lm/lm-ec.enc}{/usr/share/t exmf/fonts/enc/dvips/lm/lm-mathit.enc}{/usr/share/texmf/fonts/enc/dvips/lm/lm-m athex.enc} Output written on DiffGeo2012Skript.pdf (150 pages, 1161425 bytes). Transcript written on DiffGeo2012Skript.log. Result: ExitSuccess Running /usr/bin/makeindex DiffGeo2012Skript.idx in an env with 4 entries: This is makeindex, version 2.15 [TeX Live 2013] (kpathsea + Thai support). Scanning input file DiffGeo2012Skript.idx....done (140 entries accepted, 0 rejected). Sorting entries....done (1051 comparisons). Generating output file DiffGeo2012Skript.ind....done (216 lines written, 0 warnings). Output written in DiffGeo2012Skript.ind. Transcript written in DiffGeo2012Skript.ilg. Result: ExitSuccess Running /usr/bin/bibtex DiffGeo2012Skript.aux in an env with 4 entries: This is BibTeX, Version 0.99d (TeX Live 2013/Debian) The top-level auxiliary file: DiffGeo2012Skript.aux The style file: plain.bst Database file #1: DiffGeo2012.bib Warning--empty journal in brody1960 Warning--empty journal in olum (There were 2 warnings) Result: ExitSuccess Running /usr/bin/pdflatex DiffGeo2012Skript.tex in an env with 4 entries: This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/Debian) restricted \write18 enabled. entering extended mode (data/DiffGeo2012Skript.tex LaTeX2e <2011/06/27> Babel <3.9h> and hyphenation patterns for 78 languages loaded. 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(scrbook) I'd suggest to use (scrbook) package `scrpage2' or `scrlayer-scrpage'. (scrbook) Nevertheless, using requested (scrbook) package `fancyhdr' on input line 57. 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Underfull \hbox (badness 10000) in paragraph at lines 677--678 Underfull \hbox (badness 10000) in paragraph at lines 679--680 Underfull \hbox (badness 10000) in paragraph at lines 681--682 Underfull \vbox (badness 7168) has occurred while \output is active [7] Overfull \hbox (19.46976pt too wide) in paragraph at lines 718--719 []\T1/lmr/m/it/10.95 Eine []\T1/lmr/bx/it/10.95 dif-fe-ren-zier-ba-re Man- Underfull \hbox (badness 10000) in paragraph at lines 718--719 Underfull \hbox (badness 10000) in paragraph at lines 766--767 [8] Overfull \hbox (0.8859pt too wide) in paragraph at lines 781--781 [] Overfull \hbox (6.45883pt too wide) in paragraph at lines 794--797 []\T1/lmr/m/it/10.95 Eine ste-ti-ge Ab-bil-dung $\OML/lmm/m/it/10.95 f [] [] M \OMS/lmsy/m/n/10.95 ! Overfull \hbox (73.92368pt too wide) in paragraph at lines 855--856 []\T1/lmr/m/it/10.95 Eine Ab-bil-dung $\OML/lmm/m/it/10.95 f [] [] M \OMS/lmsy/ m/n/10.95 ! \OML/lmm/m/it/10.95 N$ \T1/lmr/m/it/10.95 heiÿt []\T1/lmr/bx/it/10. 95 Dif[]-feo[]-mor[]-phis[]-mus\T1/lmr/m/it/10.95 , [9] Overfull \hbox (23.88373pt too wide) in paragraph at lines 886--886 [] [10] [11] [12] Kapitel 2. Overfull \hbox (16.48122pt too wide) in paragraph at lines 1005--1005 [] Overfull \hbox (4.37047pt too wide) in paragraph at lines 1034--1035 []\T1/lmr/m/it/10.95 Es sei $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/it/10.95 ei- [13] Overfull \hbox (5.21416pt too wide) in paragraph at lines 1134--1135 []\T1/lmr/m/it/10.95 Es sei $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/it/10.95 ei- [14] [15] Underfull \hbox (badness 10000) in paragraph at lines 1332--1334 Overfull \hbox (2.66713pt too wide) in paragraph at lines 1387--1387 [] [16] [17] [18] Kapitel 3. [19] Overfull \hbox (14.65828pt too wide) in paragraph at lines 1626--1626 [] [20] [21] [22] [23] [24] Kapitel 4. Overfull \hbox (3.13892pt too wide) in paragraph at lines 1956--1957 []\T1/lmr/m/n/10.95 Ist $\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 '; U\OT1/lmr/m /n/10.95 )$ \T1/lmr/m/n/10.95 ei-ne Kar-te von $\OML/lmm/m/it/10.95 M$\T1/lmr/m /n/10.95 , so sind die Ab-bil-dun-gen $\OML/lmm/m/it/10.95 U \OMS/lmsy/m/n/10.9 5 ! [] \OML/lmm/m/it/10.95 M\OMS/lmsy/m/n/10.95 j[]\OML/lmm/m/it/10.95 ; p \OM S/lmsy/m/n/10.95 7! [25] Overfull \hbox (17.45334pt too wide) in paragraph at lines 2009--2010 []\T1/lmr/m/it/10.95 Die Lie-klam-mer ist ei-ne schief-sym-me-tri-sche $[]$-bil ineare Ab-bil-dung $\OMS/lmsy/m/n/10.95 V\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.9 5 M\OT1/lmr/m/n/10.95 ) \OMS/lmsy/m/n/10.95 ^^B [26] Overfull \hbox (12.142pt too wide) in paragraph at lines 2049--2049 [] [27] LaTeX Warning: Citation `lang1995differential' on page 28 undefined on input li ne 2112. [28] (/usr/share/texmf/tex/latex/lm/omslmr.fd) Overfull \hbox (8.91791pt too wide) in paragraph at lines 2203--2203 [] Overfull \hbox (33.22739pt too wide) in paragraph at lines 2223--2224 []\T1/lmr/m/it/10.95 Ein Vek-tor-feld auf $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/it/ 10.95 hei^^Dst []\T1/lmr/bx/it/10.95 voll[]-stän[]-dig\T1/lmr/m/it/10.95 , [29] Overfull \hbox (3.79543pt too wide) in paragraph at lines 2257--2258 []\T1/lmr/m/n/10.95 Integralkurven exis-tie-ren für al- Overfull \hbox (7.98071pt too wide) in paragraph at lines 2277--2277 [] [30] [31] [32] Kapitel 5. [33] Overfull \hbox (28.94324pt too wide) in paragraph at lines 2492--2495 []\T1/lmr/m/n/10.95 Die Vek-tor-bün-del $\OML/lmm/m/it/10.95 E; E[]$ \T1/lmr/m/ n/10.95 über $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/n/10.95 hei^^Dsen []\T1/lmr/bx/n /10.95 iso-morph\T1/lmr/m/n/10.95 , wenn ein $\OML/lmm/m/it/10.95 M$\T1/lmr/m/n /10.95 -Vektor[]-bündel[]-morphismus Overfull \hbox (12.94687pt too wide) in paragraph at lines 2537--2538 []\T1/lmr/m/it/10.95 Es sei $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/it/10.95 ei-ne gl at-te Man-nig-fal-tig-keit mit ei-ner of-fe-nen Über-de-ckung $\OMS/lmsy/m/n/10 .95 f\OML/lmm/m/it/10.95 U[]\OMS/lmsy/m/n/10.95 g[]$ [34] [35] [36] Overfull \hbox (3.51917pt too wide) in paragraph at lines 2664--2666 \T1/lmr/m/n/10.95 ein Ele-ment $\OML/lmm/m/it/10.95 ' \OMS/lmsy/m/n/10.95 \OML/lmm/m/it/10.95 \OMS/lmsy/m/n/10.95 2 []\OT1/lmr/m/n/10.95 (\OML/lmm/m/i t/10.95 V[] \OMS/lmsy/m/n/10.95 \OML/lmm/m/it/10.95 V[]; W[] \OMS/lmsy/m/n/10.95 \OML/lmm/m/it/10.95 W[]\OT1/lmr/m/n/10.95 )$\T1/lmr/m/n/10.95 . Sind $\OML/lmm /m/it/10.95 V$\T1/lmr/m/n/10.95 , $\OML/lmm/m/it/10.95 W$ \T1/lmr/m/n/10.95 Vek -tor-räu-me und $\OML/lmm/m/it/10.95 '[]; [] ; '[] \OMS/lmsy/m/n/10.95 2 [37] [38] Overfull \hbox (4.49565pt too wide) in paragraph at lines 2755--2758 \OML/lmm/m/it/10.95 M$\T1/lmr/m/n/10.95 ; $\OMS/lmsy/m/n/10.95 T[]\OT1/lmr/m/n/ 10.95 (\OML/lmm/m/it/10.95 M\OT1/lmr/m/n/10.95 ) = \OMS/lmsy/m/n/10.95 V\OT1/lm r/m/n/10.95 (\OML/lmm/m/it/10.95 M\OT1/lmr/m/n/10.95 )$\T1/lmr/m/n/10.95 . Es b e-zeich-ne $\OMS/lmsy/m/n/10.95 V[]\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 M\OT 1/lmr/m/n/10.95 ) = \OMS/lmsy/m/n/10.95 T[]\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10 .95 M\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/10.95 den Raum der $\OT1/lmr/m/n/10.95 ( 0\OML/lmm/m/it/10.95 ; \OT1/lmr/m/n/10.95 1)$\T1/lmr/m/n/10.95 -Tensorfelder. (/usr/share/texlive/texmf-dist/tex/latex/ucs/data/uni-0.def) [39] [40] Package hyperref Warning: Composite letter `\textasciidieresis+s' (hyperref) not defined in PD1 encoding, (hyperref) removing `\textasciidieresis' on input line 2883. [41] [42] [43] [44] Overfull \hbox (34.08974pt too wide) in paragraph at lines 3081--3082 []\T1/lmr/m/n/10.95 Der Quo-ti-ent $\OML/lmm/m/it/10.95 H[]\OT1/lmr/m/n/10.95 ( \OML/lmm/m/it/10.95 M\OT1/lmr/m/n/10.95 ) = []$ \T1/lmr/m/n/10.95 hei^^Dst die $\OML/lmm/m/it/10.95 k$\T1/lmr/m/n/10.95 -te []\T1/lmr/bx/n/10.95 deRahm-Ko[]-h omologie[]-gruppe\T1/lmr/m/n/10.95 . [45] [46] Kapitel 6. Underfull \vbox (badness 5316) has occurred while \output is active [47] [48] [49] LaTeX Warning: Citation `boothby1986introduction' on page 50 undefined on input line 3321. [50] Overfull \hbox (1.8736pt too wide) in paragraph at lines 3365--3365 [] [51] [52] Overfull \hbox (6.56665pt too wide) in paragraph at lines 3496--3498 []\T1/lmr/m/n/10.95 Es sei $\OML/lmm/m/it/10.95 ^^M$ \T1/lmr/m/n/10.95 mi-ni-ma -le Geo-dä-ti-sche, das hei^^Dst $\OMS/lmsy/m/n/10.95 L\OT1/lmr/m/n/10.95 (\OML /lmm/m/it/10.95 ^^M\OMS/lmsy/m/n/10.95 j[]\OT1/lmr/m/n/10.95 ) = \OML/lmm/m/it/ 10.95 ^^Ut \OT1/lmr/m/n/10.95 = d(\OML/lmm/m/it/10.95 ^^M\OT1/lmr/m/n/10.95 (0) \OML/lmm/m/it/10.95 ; ^^M\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 t\OT1/lmr/m/n/ 10.95 ))$\T1/lmr/m/n/10.95 . [53] [54] Kapitel 7. [55] (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/ueuf.fd) [56] [57] [58] [59] [60] [61] Overfull \hbox (2.34628pt too wide) in paragraph at lines 3972--3973 []\T1/lmr/m/it/10.95 Auf ei-ner Rie-mann-schen Man-nig-fal-tig-keit exis-tiert Overfull \hbox (9.88931pt too wide) in paragraph at lines 3984--3984 [] [62] Overfull \hbox (13.34167pt too wide) in paragraph at lines 4020--4020 [] [63] Overfull \hbox (1.11209pt too wide) in paragraph at lines 4057--4059 []\T1/lmr/bx/n/10.95 Lokale Ko-or-di-na-ten[] \T1/lmr/m/n/10.95 Es sei $\OT1/l mr/m/n/10.95 (\OML/lmm/m/it/10.95 M; g\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/10.95 e i-ne Riem-mann-sche Man-nig-fal-tig-keit mit Levi- Overfull \hbox (4.19382pt too wide) in paragraph at lines 4085--4087 \T1/lmr/m/n/10.95 (Formale Pro-dukt-re-gel: $\OMS/lmsy/m/n/10.95 r[]\OT1/lmr/m/ n/10.95 (\OMS/lmsy/m/n/10.95 r[]\OML/lmm/m/it/10.95 Z\OT1/lmr/m/n/10.95 ) = \OM S/lmsy/m/n/10.95 r[]\OT1/lmr/m/n/10.95 (\OMS/lmsy/m/n/10.95 r\OML/lmm/m/it/10.9 5 Z\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 Y\OT1/lmr/m/n/10.95 )) = (\OMS/lmsy/ m/n/10.95 r[]\OT1/lmr/m/n/10.95 (\OMS/lmsy/m/n/10.95 r\OML/lmm/m/it/10.95 Z\OT1 /lmr/m/n/10.95 ))(\OML/lmm/m/it/10.95 Y\OT1/lmr/m/n/10.95 ) + (\OMS/lmsy/m/n/10 .95 r\OML/lmm/m/it/10.95 Z\OT1/lmr/m/n/10.95 )(\OMS/lmsy/m/n/10.95 r[]\OML/lmm/ m/it/10.95 Y\OT1/lmr/m/n/10.95 ) = [64] [65] [66] Kapitel 8. [67] [68] Overfull \hbox (1.50125pt too wide) in paragraph at lines 4316--4318 []\T1/lmr/m/n/10.95 Der De-fi-ni-ti-ons-be-reich $\OMS/lmsy/m/n/10.95 D[]$ \T1/ lmr/m/n/10.95 des geo-dä-ti-schen Flus-ses ist ei-ne of-fe-ne Men-ge in $[] \OM S/lmsy/m/n/10.95 ^^B [][] \OML/lmm/m/it/10.95 M$ [69] Underfull \vbox (badness 6396) has occurred while \output is active [70] Overfull \hbox (15.84973pt too wide) in paragraph at lines 4529--4529 [] [71] [72] Overfull \hbox (3.42616pt too wide) in paragraph at lines 4612--4612 [] [73] [74] [75] [76] Kapitel 9. [77] [78] Underfull \vbox (badness 5008) has occurred while \output is active [79] LaTeX Warning: Citation `milnor1963morsetheo' on page 80 undefined on input lin e 5116. [80] [81] [82] [83] [84] [85] [86] [87] [88] LaTeX Warning: Command \d invalid in math mode on input line 5695. [89] LaTeX Warning: Citation `Cheng1975' on page 90 undefined on input line 5750. [90] LaTeX Warning: Citation `kobayashi-nomizu1963foundations-diffgeo' on page 91 un defined on input line 5836. [91] [92] [93] Overfull \hbox (7.75755pt too wide) in paragraph at lines 6079--6081 []\T1/lmr/m/it/10.95 Es sei $\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 M; g\OT1/l mr/m/n/10.95 )$ \T1/lmr/m/it/10.95 ei-ne voll-stän-di-ge Rie-mann-sche Man- LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. [94] Overfull \hbox (13.20297pt too wide) in paragraph at lines 6137--6137 [] [95] [96] [97] [98] [99] LaTeX Warning: Citation `Cheng1975' on page 100 undefined on input line 6486. [100] [101] LaTeX Warning: Citation `Cheng1975' on page 102 undefined on input line 6642. [102] [103] [104] [105] [106] Anhang A. Overfull \hbox (6.49251pt too wide) in paragraph at lines 6959--6959 [] Overfull \hbox (33.98529pt too wide) in paragraph at lines 6979--6981 $\OML/lmm/m/it/10.95 V$ \T1/lmr/m/n/10.95 ist of-fen in $\OT1/lmr/m/n/10.95 ([] [])[]$\T1/lmr/m/n/10.95 : $\OML/lmm/m/it/10.95 V \OT1/lmr/m/n/10.95 = [][]([][] \OMS/lmsy/m/n/10.95 nf\OT1/lmr/m/n/10.95 0\OMS/lmsy/m/n/10.95 g\OT1/lmr/m/n/10 .95 )$ \T1/lmr/m/n/10.95 mit $[]\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 v[]; [] ; v[]\OT1/lmr/m/n/10.95 ) = ([](\OML/lmm/m/it/10.95 k \OMS/lmsy/m/n/10.95 ^^B \OML/lmm/m/it/10.95 k[]\OT1/lmr/m/n/10.95 ))$ [107] Overfull \hbox (30.97409pt too wide) in paragraph at lines 6992--6993 []\T1/lmr/m/n/10.95 Für $\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 v[]; [] ; v[]\ OT1/lmr/m/n/10.95 ) \OMS/lmsy/m/n/10.95 2 \OML/lmm/m/it/10.95 ^^Y[]\OT1/lmr/m/n /10.95 (\OML/lmm/m/it/10.95 U[]\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/10.95 ist $\OM L/lmm/m/it/10.95 B \OMS/lmsy/m/n/10.95 ^^N \OML/lmm/m/it/10.95 ^^Y\OT1/lmr/m/n/ 10.95 (\OML/lmm/m/it/10.95 v[]; [] ; v[]\OT1/lmr/m/n/10.95 ) = (([][] \OMS/lmsy /m/n/10.95 j[]\OT1/lmr/m/n/10.95 )[]\OML/lmm/m/it/10.95 X[]\OT1/lmr/m/n/10.95 ) []$\T1/lmr/m/n/10.95 . Overfull \hbox (11.24615pt too wide) in paragraph at lines 6992--6993 \T1/lmr/m/n/10.95 Die Dar-stel-lungs-ma-trix von $\OT1/lmr/m/n/10.95 ([][] \OMS /lmsy/m/n/10.95 j[]\OT1/lmr/m/n/10.95 )[]$ \T1/lmr/m/n/10.95 be-züg-lich $\OMS/ lmsy/m/n/10.95 f\OML/lmm/m/it/10.95 x[]\OMS/lmsy/m/n/10.95 g\OML/lmm/m/it/10.95 ; \OMS/lmsy/m/n/10.95 f\OML/lmm/m/it/10.95 y[]\OMS/lmsy/m/n/10.95 g$ \T1/lmr/m /n/10.95 hängt [108] Overfull \hbox (38.54076pt too wide) in paragraph at lines 7103--7104 []$\OML/lmm/m/it/10.95 '; $ \T1/lmr/m/n/10.95 Ho-möo-mor-phis-men, $\OT1/lmr/m /n/10.95 ^^H : \OMS/lmsy/m/n/10.95 f\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 x[] ; [] ; x[]\OT1/lmr/m/n/10.95 ) \OMS/lmsy/m/n/10.95 2 [][] j \OML/lmm/m/it/10.95 x[] < \OT1/lmr/m/n/10.95 1\OMS/lmsy/m/n/10.95 g ! [][]\OML/lmm/m/it/10.95 ; x \OMS/lmsy/m/n/10.95 7! []\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 x[]; [] ; x[]\ OT1/lmr/m/n/10.95 ) \OMS/lmsy/m/n/10.95 ) [109] Overfull \hbox (10.38538pt too wide) in paragraph at lines 7171--7171 [] [110]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7251 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7257 \begin{Aufg} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b] [111]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7272 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.4}) has been already used, duplicate ignored \relax l.7278 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.7282 \begin{Loes} [112]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.7324 \begin{Loes} \begin{enumerate}[label=\alph*),widest=b,leftmargin=*] [113]pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.7378 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.4}) has been already used, duplicate ignored \relax l.7419 \begin{Loes} [114]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7447 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7458 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7473 \begin{Aufg} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b] [115]pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.7480 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.2}) has been already used, duplicate ignored \relax l.7518 \begin{Loes} \begin{enumerate}[label=\alph*),leftmargin=*,widest=a] [116]pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.7550 \begin{Loes} \begin{enumerate}[label=\alph*),widest=a,leftmargin=*] [117]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7589 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7600 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7610 \begin{Aufg} [118]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.4}) has been already used, duplicate ignored \relax l.7616 \begin{Aufg} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b]pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been a lready used, duplicate ignored \relax l.7625 \begin{Loes} [119]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.7664 \begin{Loes} Overfull \hbox (39.6498pt too wide) in paragraph at lines 7679--7679 [][] [120]pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.7721 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.4}) has been already used, duplicate ignored \relax l.7751 \begin{Loes} \begin{enumerate}[label=(\alph*),leftmargin=*,widest=a] [121]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7783 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7788 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7801 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.7811 \begin{Loes} \label{exc:ueb5-a1} [122] [123] Overfull \hbox (30.3387pt too wide) in paragraph at lines 7867--7868 []\T1/lmr/m/n/10.95 lokale Ko-or-di-na-ten $\U/msa/m/n/10.95 []\OML/lmm/m/it/ 10.95 x[]$\T1/lmr/m/n/10.95 , Ko-ef-fi-zi-en-ten von $\OML/lmm/m/it/10.95 ![]; [] ; X[]$ pdfTeX warning (ext4): destination with the same identifier (name{Loes.2}) has been already used, duplicate ignored \relax l.7895 \begin{Loes} \begin{enumerate}[label=\alph*), leftmargin=*] [124]pdfTeX w arning (ext4): destination with the same identifier (name{Loes.3}) has been alr eady used, duplicate ignored \relax l.7910 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7935 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7946 \begin{Aufg} Overfull \hbox (8.36499pt too wide) in paragraph at lines 7953--7954 []\T1/lmr/m/n/10.95 Die Rie-mann-sche Man-nig-fal-tig-keit $\OT1/lmr/m/n/10.95 (\U/msb/m/n/10.95 H[]\OML/lmm/m/it/10.95 ; g\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/1 0.95 heiÿt $\OML/lmm/m/it/10.95 n$\T1/lmr/m/it/10.95 -dimensionaler hy-per-bo-l i-scher Raum\T1/lmr/m/n/10.95 . pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7956 \begin{Aufg} [125]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.1}) has been already used, duplicate ignored \relax l.7967 \begin{Loes} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b]pdfTeX warning (ext4): destination with the same identifier (name{Loes.2}) has been a lready used, duplicate ignored \relax l.7974 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.7978 \begin{Loes} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been a lready used, duplicate ignored \relax l.7996 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8002 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.8012 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.8024 \begin{Loes} [126]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.8052 \begin{Loes} [127] [128] Overfull \hbox (6.37263pt too wide) in paragraph at lines 8109--8111 []$\OMS/lmsy/m/n/10.95 r[]$ \T1/lmr/m/n/10.95 ist der []\T1/lmr/bx/n/10.95 Levi -Civita Zu-sam-men-hang \T1/lmr/m/n/10.95 von $\OT1/lmr/m/n/10.95 (\OML/lmm/m/i t/10.95 M; g\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/10.95 mit $\OML/lmm/m/it/10.95 g\ OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 X; Y\OT1/lmr/m/n/10.95 ) = pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.8115 \begin{Loes} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been a lready used, duplicate ignored \relax l.8153 \begin{Aufg} [129]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8163 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.8175 \begin{Aufg} Overfull \hbox (35.37292pt too wide) in paragraph at lines 8207--8207 [] Underfull \vbox (badness 10000) has occurred while \output is active [130]pdfTe X warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.8211 \begin{Loes} [131]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.8241 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.8277 \begin{Loes} [132]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.8297 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8303 \begin{Aufg} Overfull \hbox (18.51144pt too wide) in paragraph at lines 8304--8305 []\T1/lmr/m/n/10.95 Bestimmen Sie die Schnitt-krüm-mun-gen der Rie-mann-schen M an-nig-fal-tig-kei-ten $\OT1/lmr/m/n/10.95 ([][]\OML/lmm/m/it/10.95 ; g[]\OT1/l mr/m/n/10.95 )$ pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.8307 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.8313 \begin{Loes} [133]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.8377 \begin{Loes} \begin{enumerate}[label=\alph*), widest=b, leftmargin=*]\... [134] Overfull \hbox (19.2354pt too wide) in paragraph at lines 8401--8402 []\T1/lmr/m/n/10.95 Wir be-rech-nen die Kom-po-nen-ten $\OML/lmm/m/it/10.95 R[] \OT1/lmr/m/n/10.95 = \OML/lmm/m/it/10.95 R\OT1/lmr/m/n/10.95 ([]\OML/lmm/m/it/ 10.95 ; []; []; []\OT1/lmr/m/n/10.95 ) = \OML/lmm/m/it/10.95 g\OT1/lmr/m/n/10.9 5 (\OML/lmm/m/it/10.95 R\OT1/lmr/m/n/10.95 ([]\OML/lmm/m/it/10.95 ; []\OT1/lmr/ m/n/10.95 )[]\OML/lmm/m/it/10.95 ; []\OT1/lmr/m/n/10.95 )$ Overfull \hbox (13.04242pt too wide) in paragraph at lines 8411--8411 [] Overfull \hbox (36.99953pt too wide) in paragraph at lines 8420--8420 [] Underfull \vbox (badness 1755) has occurred while \output is active [135] Overfull \hbox (100.82646pt too wide) in paragraph at lines 8442--8442 [] Overfull \hbox (26.51044pt too wide) in paragraph at lines 8457--8457 [] [136]pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.8462 \begin{Loes} Overfull \hbox (26.24988pt too wide) in paragraph at lines 8492--8492 [] Underfull \vbox (badness 10000) has occurred while \output is active [137] [138] [139] [140] [141]pdfTeX warning (ext4): destination with the same identif ier (name{Aufg.1}) has been already used, duplicate ignored \relax l.8719 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8730 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.8736 \begin{Loes} [142]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.8776 \begin{Loes} \begin{description}[leftmargin=*] LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . 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Underfull \hbox (badness 10000) in paragraph at lines 677--678 Underfull \hbox (badness 10000) in paragraph at lines 679--680 Underfull \hbox (badness 10000) in paragraph at lines 681--682 Underfull \vbox (badness 7168) has occurred while \output is active [7] Overfull \hbox (19.46976pt too wide) in paragraph at lines 718--719 []\T1/lmr/m/it/10.95 Eine []\T1/lmr/bx/it/10.95 dif-fe-ren-zier-ba-re Man- Underfull \hbox (badness 10000) in paragraph at lines 718--719 Underfull \hbox (badness 10000) in paragraph at lines 766--767 [8] Overfull \hbox (0.8859pt too wide) in paragraph at lines 781--781 [] Overfull \hbox (6.45883pt too wide) in paragraph at lines 794--797 []\T1/lmr/m/it/10.95 Eine ste-ti-ge Ab-bil-dung $\OML/lmm/m/it/10.95 f [] [] M \OMS/lmsy/m/n/10.95 ! Overfull \hbox (73.92368pt too wide) in paragraph at lines 855--856 []\T1/lmr/m/it/10.95 Eine Ab-bil-dung $\OML/lmm/m/it/10.95 f [] [] M \OMS/lmsy/ m/n/10.95 ! \OML/lmm/m/it/10.95 N$ \T1/lmr/m/it/10.95 heiÿt []\T1/lmr/bx/it/10. 95 Dif[]-feo[]-mor[]-phis[]-mus\T1/lmr/m/it/10.95 , [9] Overfull \hbox (23.88373pt too wide) in paragraph at lines 886--886 [] [10] [11] [12] Kapitel 2. Overfull \hbox (16.48122pt too wide) in paragraph at lines 1005--1005 [] Overfull \hbox (4.37047pt too wide) in paragraph at lines 1034--1035 []\T1/lmr/m/it/10.95 Es sei $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/it/10.95 ei- [13] Overfull \hbox (5.21416pt too wide) in paragraph at lines 1134--1135 []\T1/lmr/m/it/10.95 Es sei $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/it/10.95 ei- [14] [15] Underfull \hbox (badness 10000) in paragraph at lines 1332--1334 Overfull \hbox (2.66713pt too wide) in paragraph at lines 1387--1387 [] [16] [17] [18] Kapitel 3. [19] Overfull \hbox (14.65828pt too wide) in paragraph at lines 1626--1626 [] [20] [21] [22] [23] [24] Kapitel 4. Overfull \hbox (3.13892pt too wide) in paragraph at lines 1956--1957 []\T1/lmr/m/n/10.95 Ist $\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 '; U\OT1/lmr/m /n/10.95 )$ \T1/lmr/m/n/10.95 ei-ne Kar-te von $\OML/lmm/m/it/10.95 M$\T1/lmr/m /n/10.95 , so sind die Ab-bil-dun-gen $\OML/lmm/m/it/10.95 U \OMS/lmsy/m/n/10.9 5 ! [] \OML/lmm/m/it/10.95 M\OMS/lmsy/m/n/10.95 j[]\OML/lmm/m/it/10.95 ; p \OM S/lmsy/m/n/10.95 7! [25] Overfull \hbox (17.45334pt too wide) in paragraph at lines 2009--2010 []\T1/lmr/m/it/10.95 Die Lie-klam-mer ist ei-ne schief-sym-me-tri-sche $[]$-bil ineare Ab-bil-dung $\OMS/lmsy/m/n/10.95 V\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.9 5 M\OT1/lmr/m/n/10.95 ) \OMS/lmsy/m/n/10.95 ^^B [26] Overfull \hbox (12.142pt too wide) in paragraph at lines 2049--2049 [] [27] [28] (/usr/share/texmf/tex/latex/lm/omslmr.fd) Overfull \hbox (8.91791pt too wide) in paragraph at lines 2203--2203 [] Overfull \hbox (33.22739pt too wide) in paragraph at lines 2223--2224 []\T1/lmr/m/it/10.95 Ein Vek-tor-feld auf $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/it/ 10.95 hei^^Dst []\T1/lmr/bx/it/10.95 voll[]-stän[]-dig\T1/lmr/m/it/10.95 , [29] Overfull \hbox (3.79543pt too wide) in paragraph at lines 2257--2258 []\T1/lmr/m/n/10.95 Integralkurven exis-tie-ren für al- Overfull \hbox (7.98071pt too wide) in paragraph at lines 2277--2277 [] [30] [31] [32] Kapitel 5. [33] Overfull \hbox (28.94324pt too wide) in paragraph at lines 2492--2495 []\T1/lmr/m/n/10.95 Die Vek-tor-bün-del $\OML/lmm/m/it/10.95 E; E[]$ \T1/lmr/m/ n/10.95 über $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/n/10.95 hei^^Dsen []\T1/lmr/bx/n /10.95 iso-morph\T1/lmr/m/n/10.95 , wenn ein $\OML/lmm/m/it/10.95 M$\T1/lmr/m/n /10.95 -Vektor[]-bündel[]-morphismus Overfull \hbox (12.94687pt too wide) in paragraph at lines 2537--2538 []\T1/lmr/m/it/10.95 Es sei $\OML/lmm/m/it/10.95 M$ \T1/lmr/m/it/10.95 ei-ne gl at-te Man-nig-fal-tig-keit mit ei-ner of-fe-nen Über-de-ckung $\OMS/lmsy/m/n/10 .95 f\OML/lmm/m/it/10.95 U[]\OMS/lmsy/m/n/10.95 g[]$ [34] [35] [36] Overfull \hbox (3.51917pt too wide) in paragraph at lines 2664--2666 \T1/lmr/m/n/10.95 ein Ele-ment $\OML/lmm/m/it/10.95 ' \OMS/lmsy/m/n/10.95 \OML/lmm/m/it/10.95 \OMS/lmsy/m/n/10.95 2 []\OT1/lmr/m/n/10.95 (\OML/lmm/m/i t/10.95 V[] \OMS/lmsy/m/n/10.95 \OML/lmm/m/it/10.95 V[]; W[] \OMS/lmsy/m/n/10.95 \OML/lmm/m/it/10.95 W[]\OT1/lmr/m/n/10.95 )$\T1/lmr/m/n/10.95 . Sind $\OML/lmm /m/it/10.95 V$\T1/lmr/m/n/10.95 , $\OML/lmm/m/it/10.95 W$ \T1/lmr/m/n/10.95 Vek -tor-räu-me und $\OML/lmm/m/it/10.95 '[]; [] ; '[] \OMS/lmsy/m/n/10.95 2 [37] [38] Overfull \hbox (4.49565pt too wide) in paragraph at lines 2755--2758 \OML/lmm/m/it/10.95 M$\T1/lmr/m/n/10.95 ; $\OMS/lmsy/m/n/10.95 T[]\OT1/lmr/m/n/ 10.95 (\OML/lmm/m/it/10.95 M\OT1/lmr/m/n/10.95 ) = \OMS/lmsy/m/n/10.95 V\OT1/lm r/m/n/10.95 (\OML/lmm/m/it/10.95 M\OT1/lmr/m/n/10.95 )$\T1/lmr/m/n/10.95 . Es b e-zeich-ne $\OMS/lmsy/m/n/10.95 V[]\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 M\OT 1/lmr/m/n/10.95 ) = \OMS/lmsy/m/n/10.95 T[]\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10 .95 M\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/10.95 den Raum der $\OT1/lmr/m/n/10.95 ( 0\OML/lmm/m/it/10.95 ; \OT1/lmr/m/n/10.95 1)$\T1/lmr/m/n/10.95 -Tensorfelder. (/usr/share/texlive/texmf-dist/tex/latex/ucs/data/uni-0.def) [39] [40] Package hyperref Warning: Composite letter `\textasciidieresis+s' (hyperref) not defined in PD1 encoding, (hyperref) removing `\textasciidieresis' on input line 2883. [41] [42] [43] [44] Overfull \hbox (34.08974pt too wide) in paragraph at lines 3081--3082 []\T1/lmr/m/n/10.95 Der Quo-ti-ent $\OML/lmm/m/it/10.95 H[]\OT1/lmr/m/n/10.95 ( \OML/lmm/m/it/10.95 M\OT1/lmr/m/n/10.95 ) = []$ \T1/lmr/m/n/10.95 hei^^Dst die $\OML/lmm/m/it/10.95 k$\T1/lmr/m/n/10.95 -te []\T1/lmr/bx/n/10.95 deRahm-Ko[]-h omologie[]-gruppe\T1/lmr/m/n/10.95 . [45] [46] Kapitel 6. Underfull \vbox (badness 5316) has occurred while \output is active [47] [48] [49] [50] Overfull \hbox (1.8736pt too wide) in paragraph at lines 3365--3365 [] [51] [52] Overfull \hbox (6.56665pt too wide) in paragraph at lines 3496--3498 []\T1/lmr/m/n/10.95 Es sei $\OML/lmm/m/it/10.95 ^^M$ \T1/lmr/m/n/10.95 mi-ni-ma -le Geo-dä-ti-sche, das hei^^Dst $\OMS/lmsy/m/n/10.95 L\OT1/lmr/m/n/10.95 (\OML /lmm/m/it/10.95 ^^M\OMS/lmsy/m/n/10.95 j[]\OT1/lmr/m/n/10.95 ) = \OML/lmm/m/it/ 10.95 ^^Ut \OT1/lmr/m/n/10.95 = d(\OML/lmm/m/it/10.95 ^^M\OT1/lmr/m/n/10.95 (0) \OML/lmm/m/it/10.95 ; ^^M\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 t\OT1/lmr/m/n/ 10.95 ))$\T1/lmr/m/n/10.95 . [53] [54] Kapitel 7. [55] (/usr/share/texlive/texmf-dist/tex/latex/amsfonts/ueuf.fd) [56] [57] [58] [59] [60] [61] Overfull \hbox (2.34628pt too wide) in paragraph at lines 3972--3973 []\T1/lmr/m/it/10.95 Auf ei-ner Rie-mann-schen Man-nig-fal-tig-keit exis-tiert Overfull \hbox (9.88931pt too wide) in paragraph at lines 3984--3984 [] [62] Overfull \hbox (13.34167pt too wide) in paragraph at lines 4020--4020 [] [63] Overfull \hbox (1.11209pt too wide) in paragraph at lines 4057--4059 []\T1/lmr/bx/n/10.95 Lokale Ko-or-di-na-ten[] \T1/lmr/m/n/10.95 Es sei $\OT1/l mr/m/n/10.95 (\OML/lmm/m/it/10.95 M; g\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/10.95 e i-ne Riem-mann-sche Man-nig-fal-tig-keit mit Levi- Overfull \hbox (4.19382pt too wide) in paragraph at lines 4085--4087 \T1/lmr/m/n/10.95 (Formale Pro-dukt-re-gel: $\OMS/lmsy/m/n/10.95 r[]\OT1/lmr/m/ n/10.95 (\OMS/lmsy/m/n/10.95 r[]\OML/lmm/m/it/10.95 Z\OT1/lmr/m/n/10.95 ) = \OM S/lmsy/m/n/10.95 r[]\OT1/lmr/m/n/10.95 (\OMS/lmsy/m/n/10.95 r\OML/lmm/m/it/10.9 5 Z\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 Y\OT1/lmr/m/n/10.95 )) = (\OMS/lmsy/ m/n/10.95 r[]\OT1/lmr/m/n/10.95 (\OMS/lmsy/m/n/10.95 r\OML/lmm/m/it/10.95 Z\OT1 /lmr/m/n/10.95 ))(\OML/lmm/m/it/10.95 Y\OT1/lmr/m/n/10.95 ) + (\OMS/lmsy/m/n/10 .95 r\OML/lmm/m/it/10.95 Z\OT1/lmr/m/n/10.95 )(\OMS/lmsy/m/n/10.95 r[]\OML/lmm/ m/it/10.95 Y\OT1/lmr/m/n/10.95 ) = [64] [65] [66] Kapitel 8. [67] [68] Overfull \hbox (1.50125pt too wide) in paragraph at lines 4316--4318 []\T1/lmr/m/n/10.95 Der De-fi-ni-ti-ons-be-reich $\OMS/lmsy/m/n/10.95 D[]$ \T1/ lmr/m/n/10.95 des geo-dä-ti-schen Flus-ses ist ei-ne of-fe-ne Men-ge in $[] \OM S/lmsy/m/n/10.95 ^^B [][] \OML/lmm/m/it/10.95 M$ [69] Underfull \vbox (badness 6396) has occurred while \output is active [70] Overfull \hbox (15.84973pt too wide) in paragraph at lines 4529--4529 [] [71] [72] Overfull \hbox (3.42616pt too wide) in paragraph at lines 4612--4612 [] [73] [74] [75] [76] Kapitel 9. [77] [78] Underfull \vbox (badness 5008) has occurred while \output is active [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] LaTeX Warning: Command \d invalid in math mode on input line 5695. [89] [90] [91] [92] [93] Overfull \hbox (7.75755pt too wide) in paragraph at lines 6079--6081 []\T1/lmr/m/it/10.95 Es sei $\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 M; g\OT1/l mr/m/n/10.95 )$ \T1/lmr/m/it/10.95 ei-ne voll-stän-di-ge Rie-mann-sche Man- LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. LaTeX Warning: Command \" invalid in math mode on input line 6109. [94] Overfull \hbox (13.20297pt too wide) in paragraph at lines 6137--6137 [] [95] [96] [97] [98] [99] [100] [101] [102] [103] [104] [105] [106] Anhang A. Overfull \hbox (6.49251pt too wide) in paragraph at lines 6959--6959 [] Overfull \hbox (33.98529pt too wide) in paragraph at lines 6979--6981 $\OML/lmm/m/it/10.95 V$ \T1/lmr/m/n/10.95 ist of-fen in $\OT1/lmr/m/n/10.95 ([] [])[]$\T1/lmr/m/n/10.95 : $\OML/lmm/m/it/10.95 V \OT1/lmr/m/n/10.95 = [][]([][] \OMS/lmsy/m/n/10.95 nf\OT1/lmr/m/n/10.95 0\OMS/lmsy/m/n/10.95 g\OT1/lmr/m/n/10 .95 )$ \T1/lmr/m/n/10.95 mit $[]\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 v[]; [] ; v[]\OT1/lmr/m/n/10.95 ) = ([](\OML/lmm/m/it/10.95 k \OMS/lmsy/m/n/10.95 ^^B \OML/lmm/m/it/10.95 k[]\OT1/lmr/m/n/10.95 ))$ [107] Overfull \hbox (30.97409pt too wide) in paragraph at lines 6992--6993 []\T1/lmr/m/n/10.95 Für $\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 v[]; [] ; v[]\ OT1/lmr/m/n/10.95 ) \OMS/lmsy/m/n/10.95 2 \OML/lmm/m/it/10.95 ^^Y[]\OT1/lmr/m/n /10.95 (\OML/lmm/m/it/10.95 U[]\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/10.95 ist $\OM L/lmm/m/it/10.95 B \OMS/lmsy/m/n/10.95 ^^N \OML/lmm/m/it/10.95 ^^Y\OT1/lmr/m/n/ 10.95 (\OML/lmm/m/it/10.95 v[]; [] ; v[]\OT1/lmr/m/n/10.95 ) = (([][] \OMS/lmsy /m/n/10.95 j[]\OT1/lmr/m/n/10.95 )[]\OML/lmm/m/it/10.95 X[]\OT1/lmr/m/n/10.95 ) []$\T1/lmr/m/n/10.95 . Overfull \hbox (11.24615pt too wide) in paragraph at lines 6992--6993 \T1/lmr/m/n/10.95 Die Dar-stel-lungs-ma-trix von $\OT1/lmr/m/n/10.95 ([][] \OMS /lmsy/m/n/10.95 j[]\OT1/lmr/m/n/10.95 )[]$ \T1/lmr/m/n/10.95 be-züg-lich $\OMS/ lmsy/m/n/10.95 f\OML/lmm/m/it/10.95 x[]\OMS/lmsy/m/n/10.95 g\OML/lmm/m/it/10.95 ; \OMS/lmsy/m/n/10.95 f\OML/lmm/m/it/10.95 y[]\OMS/lmsy/m/n/10.95 g$ \T1/lmr/m /n/10.95 hängt [108] Overfull \hbox (38.54076pt too wide) in paragraph at lines 7103--7104 []$\OML/lmm/m/it/10.95 '; $ \T1/lmr/m/n/10.95 Ho-möo-mor-phis-men, $\OT1/lmr/m /n/10.95 ^^H : \OMS/lmsy/m/n/10.95 f\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 x[] ; [] ; x[]\OT1/lmr/m/n/10.95 ) \OMS/lmsy/m/n/10.95 2 [][] j \OML/lmm/m/it/10.95 x[] < \OT1/lmr/m/n/10.95 1\OMS/lmsy/m/n/10.95 g ! [][]\OML/lmm/m/it/10.95 ; x \OMS/lmsy/m/n/10.95 7! []\OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 x[]; [] ; x[]\ OT1/lmr/m/n/10.95 ) \OMS/lmsy/m/n/10.95 ) [109] Overfull \hbox (10.38538pt too wide) in paragraph at lines 7171--7171 [] [110]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7251 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7257 \begin{Aufg} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b] [111]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7272 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.4}) has been already used, duplicate ignored \relax l.7278 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.7282 \begin{Loes} [112]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.7324 \begin{Loes} \begin{enumerate}[label=\alph*),widest=b,leftmargin=*] [113]pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.7378 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.4}) has been already used, duplicate ignored \relax l.7419 \begin{Loes} [114]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7447 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7458 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7473 \begin{Aufg} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b] [115]pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.7480 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.2}) has been already used, duplicate ignored \relax l.7518 \begin{Loes} \begin{enumerate}[label=\alph*),leftmargin=*,widest=a] [116]pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.7550 \begin{Loes} \begin{enumerate}[label=\alph*),widest=a,leftmargin=*] [117]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7589 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7600 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7610 \begin{Aufg} [118]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.4}) has been already used, duplicate ignored \relax l.7616 \begin{Aufg} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b]pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been a lready used, duplicate ignored \relax l.7625 \begin{Loes} [119]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.7664 \begin{Loes} Overfull \hbox (39.6498pt too wide) in paragraph at lines 7679--7679 [][] [120]pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.7721 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.4}) has been already used, duplicate ignored \relax l.7751 \begin{Loes} \begin{enumerate}[label=(\alph*),leftmargin=*,widest=a] [121]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7783 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7788 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7801 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.7811 \begin{Loes} \label{exc:ueb5-a1} [122] [123] Overfull \hbox (30.3387pt too wide) in paragraph at lines 7867--7868 []\T1/lmr/m/n/10.95 lokale Ko-or-di-na-ten $\U/msa/m/n/10.95 []\OML/lmm/m/it/ 10.95 x[]$\T1/lmr/m/n/10.95 , Ko-ef-fi-zi-en-ten von $\OML/lmm/m/it/10.95 ![]; [] ; X[]$ pdfTeX warning (ext4): destination with the same identifier (name{Loes.2}) has been already used, duplicate ignored \relax l.7895 \begin{Loes} \begin{enumerate}[label=\alph*), leftmargin=*] [124]pdfTeX w arning (ext4): destination with the same identifier (name{Loes.3}) has been alr eady used, duplicate ignored \relax l.7910 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.7935 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.7946 \begin{Aufg} Overfull \hbox (8.36499pt too wide) in paragraph at lines 7953--7954 []\T1/lmr/m/n/10.95 Die Rie-mann-sche Man-nig-fal-tig-keit $\OT1/lmr/m/n/10.95 (\U/msb/m/n/10.95 H[]\OML/lmm/m/it/10.95 ; g\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/1 0.95 heiÿt $\OML/lmm/m/it/10.95 n$\T1/lmr/m/it/10.95 -dimensionaler hy-per-bo-l i-scher Raum\T1/lmr/m/n/10.95 . pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.7956 \begin{Aufg} [125]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.1}) has been already used, duplicate ignored \relax l.7967 \begin{Loes} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b]pdfTeX warning (ext4): destination with the same identifier (name{Loes.2}) has been a lready used, duplicate ignored \relax l.7974 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.7978 \begin{Loes} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been a lready used, duplicate ignored \relax l.7996 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8002 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.8012 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.8024 \begin{Loes} [126]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.8052 \begin{Loes} [127] [128] Overfull \hbox (6.37263pt too wide) in paragraph at lines 8109--8111 []$\OMS/lmsy/m/n/10.95 r[]$ \T1/lmr/m/n/10.95 ist der []\T1/lmr/bx/n/10.95 Levi -Civita Zu-sam-men-hang \T1/lmr/m/n/10.95 von $\OT1/lmr/m/n/10.95 (\OML/lmm/m/i t/10.95 M; g\OT1/lmr/m/n/10.95 )$ \T1/lmr/m/n/10.95 mit $\OML/lmm/m/it/10.95 g\ OT1/lmr/m/n/10.95 (\OML/lmm/m/it/10.95 X; Y\OT1/lmr/m/n/10.95 ) = pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.8115 \begin{Loes} \begin{enumerate}[label=\alph*),leftmargin=*,widest=b]pdfTeX warning (ext4): destination with the same identifier (name{Aufg.1}) has been a lready used, duplicate ignored \relax l.8153 \begin{Aufg} [129]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8163 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.8175 \begin{Aufg} Overfull \hbox (35.37292pt too wide) in paragraph at lines 8207--8207 [] Underfull \vbox (badness 10000) has occurred while \output is active [130]pdfTe X warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.8211 \begin{Loes} [131]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.8241 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.8277 \begin{Loes} [132]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.8297 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8303 \begin{Aufg} Overfull \hbox (18.51144pt too wide) in paragraph at lines 8304--8305 []\T1/lmr/m/n/10.95 Bestimmen Sie die Schnitt-krüm-mun-gen der Rie-mann-schen M an-nig-fal-tig-kei-ten $\OT1/lmr/m/n/10.95 ([][]\OML/lmm/m/it/10.95 ; g[]\OT1/l mr/m/n/10.95 )$ pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.8307 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.8313 \begin{Loes} [133]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.8377 \begin{Loes} \begin{enumerate}[label=\alph*), widest=b, leftmargin=*]\... [134] Overfull \hbox (19.2354pt too wide) in paragraph at lines 8401--8402 []\T1/lmr/m/n/10.95 Wir be-rech-nen die Kom-po-nen-ten $\OML/lmm/m/it/10.95 R[] \OT1/lmr/m/n/10.95 = \OML/lmm/m/it/10.95 R\OT1/lmr/m/n/10.95 ([]\OML/lmm/m/it/ 10.95 ; []; []; []\OT1/lmr/m/n/10.95 ) = \OML/lmm/m/it/10.95 g\OT1/lmr/m/n/10.9 5 (\OML/lmm/m/it/10.95 R\OT1/lmr/m/n/10.95 ([]\OML/lmm/m/it/10.95 ; []\OT1/lmr/ m/n/10.95 )[]\OML/lmm/m/it/10.95 ; []\OT1/lmr/m/n/10.95 )$ Overfull \hbox (13.04242pt too wide) in paragraph at lines 8411--8411 [] Overfull \hbox (36.99953pt too wide) in paragraph at lines 8420--8420 [] Underfull \vbox (badness 1755) has occurred while \output is active [135] Overfull \hbox (100.82646pt too wide) in paragraph at lines 8442--8442 [] Overfull \hbox (26.51044pt too wide) in paragraph at lines 8457--8457 [] [136]pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.8462 \begin{Loes} Overfull \hbox (26.24988pt too wide) in paragraph at lines 8492--8492 [] Underfull \vbox (badness 10000) has occurred while \output is active [137] [138] [139] [140] [141]pdfTeX warning (ext4): destination with the same identif ier (name{Aufg.1}) has been already used, duplicate ignored \relax l.8719 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8730 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Loes.1}) has been already used, duplicate ignored \relax l.8736 \begin{Loes} [142]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.8776 \begin{Loes} \begin{description}[leftmargin=*] LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . LaTeX Font Warning: Command \scriptsize invalid in math mode on input line 8798 . [143] [144]pdfTeX warning (ext4): destination with the same identifier (name{Au fg.1}) has been already used, duplicate ignored \relax l.8901 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.8909 \begin{Aufg} [145]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.1}) has been already used, duplicate ignored \relax l.8934 \begin{Loes} [146]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.2}) has been already used, duplicate ignored \relax l.8987 \begin{Loes} [147]pdfTeX warning (ext4): destination with the same ident ifier (name{Aufg.1}) has been already used, duplicate ignored \relax l.9083 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.2}) has been already used, duplicate ignored \relax l.9091 \begin{Aufg} pdfTeX warning (ext4): destination with the same identifier (name{Aufg.3}) has been already used, duplicate ignored \relax l.9095 \begin{Aufg} [148]pdfTeX warning (ext4): destination with the same ident ifier (name{Loes.1}) has been already used, duplicate ignored \relax l.9099 \begin{Loes} \begin{description}[leftmargin=*] [149]pdfTeX warning (ext4) : destination with the same identifier (name{Loes.2}) has been already used, du plicate ignored \relax l.9156 \begin{Loes} pdfTeX warning (ext4): destination with the same identifier (name{Loes.3}) has been already used, duplicate ignored \relax l.9161 \begin{Loes} Overfull \hbox (0.37314pt too wide) in paragraph at lines 9181--9181 [] Overfull \hbox (0.37314pt too wide) in paragraph at lines 9207--9207 [] (./DiffGeo2012Skript.ind [150] [151] [152]) No file DiffGeo2012Skript.gls. (./DiffGeo2012Skript.bbl [153] [154]) [155] (./DiffGeo2012Skript.aux) LaTeX Font Warning: Some font shapes were not available, defaults substituted. ) (see the transcript file for additional information)pdfTeX warning (dest): name {glo:spur} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Dualraum} has been referenced but does not exis t, replaced by a fixed one pdfTeX warning (dest): name{glo:GL} has been referenced but does not exist, rep laced by a fixed one pdfTeX warning (dest): name{glo:Homomorphismus} has been referenced but does no t exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Isomorphismus} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{glo:supp} has been referenced but does not exist, r eplaced by a fixed one pdfTeX warning (dest): name{glo:Kurve} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Produkttopologie} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Endomorphismus} has been referenced but does no t exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Diffeomorphismus} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Homoeomorphismus} has been referenced but does not exist, replaced by a fixed one pdfTeX warning (dest): name{glo:Topologie} has been referenced but does not exi st, replaced by a fixed one pdfTeX warning (dest): name{glo:Hausdorff-Raum} has been referenced but does no t exist, replaced by a fixed one {/usr/share/texmf/fonts/enc/dvips/lm/lm-rm.enc}{/usr/share/texmf/fonts/enc/dvip s/lm/lm-mathsy.enc}{/usr/share/texmf/fonts/enc/dvips/lm/lm-ec.enc}{/usr/share/t exmf/fonts/enc/dvips/lm/lm-mathit.enc}{/usr/share/texmf/fonts/enc/dvips/lm/lm-m athex.enc} Output written on DiffGeo2012Skript.pdf (155 pages, 1182409 bytes). Transcript written on DiffGeo2012Skript.log. Result: ExitSuccess Running /usr/bin/convert -verbose DiffGeo2012Skript.pdf[0] -resize 70x DiffGeo2012Skript.png in an env with 4 entries: "gs" -q -dQUIET -dSAFER -dBATCH -dNOPAUSE -dNOPROMPT -dMaxBitmap=500000000 -dAlignToPixels=0 -dGridFitTT=2 "-sDEVICE=pngalpha" -dTextAlphaBits=4 -dGraphicsAlphaBits=4 "-r72x72" -dFirstPage=1 -dLastPage=1 "-sOutputFile=/tmp/magick-MLSYD7gc-%08d" "-f/tmp/magick-PaLIEPRg" "-f/tmp/magick-3cU0DEsl" /tmp/magick-MLSYD7gc-00000001 PNG 595x842 595x842+0+0 8-bit DirectClass 15.3KB 0.010u 0:00.010 DiffGeo2012Skript.pdf[0]=>DiffGeo2012Skript.pdf PDF 595x842 595x842+0+0 16-bit DirectClass 15.3KB 0.000u 0:00.000 DiffGeo2012Skript.pdf[0]=>DiffGeo2012Skript.png PDF 595x842=>70x99 70x99+0+0 16-bit DirectClass 0.040u 0:00.019 Result: ExitSuccess Running /usr/bin/optipng -verbose DiffGeo2012Skript.png in an env with 4 entries: OptiPNG 0.6.4: Advanced PNG optimizer. Copyright (C) 2001-2010 Cosmin Truta. ** Processing: DiffGeo2012Skript.png 70x99 pixels, 4x16 bits/pixel, RGB+alpha Input IDAT size = 2069 bytes Input file size = 2368 bytes Trying: zc = 9 zm = 8 zs = 0 f = 0 IDAT size = 1895 zc = 9 zm = 8 zs = 1 f = 0 IDAT too big zc = 1 zm = 8 zs = 2 f = 0 IDAT too big zc = 9 zm = 8 zs = 3 f = 0 IDAT too big zc = 9 zm = 8 zs = 0 f = 5 IDAT too big zc = 9 zm = 8 zs = 1 f = 5 IDAT too big zc = 1 zm = 8 zs = 2 f = 5 IDAT too big zc = 9 zm = 8 zs = 3 f = 5 IDAT size = 1895 Selecting parameters: zc = 9 zm = 8 zs = 3 f = 5 IDAT size = 1895 Output IDAT size = 1895 bytes (174 bytes decrease) Output file size = 2194 bytes (174 bytes = 7.35% decrease) ** Status report 1 file(s) have been processed. Result: ExitSuccess