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differentialgeometry15

differentialgeometry15 - Comvosmsfions MGM K mm H we’...

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Unformatted text preview: Comvosmsfions MGM K mm! H we’ have, now \QQJ‘ALA '\'\’\0\\_ 2 K g e3? (wk (QMSE)- 225:? [56- F2 H = :1 (EG—- F1) J mu; (Sven n‘xcfi Qormohe. {30? We. E3EG’QAA 6&3. E : <Xofl<o> e“: <XU,NU> F : <X03Kv> Q : Z<xusNV> 6—= <xhxq> ‘3: <X«,M\r> (AL wm‘v *0 see. MOD; Am AroyA same. geomekdc. impormm’fi‘on 'prom “Mat. Obsamoén‘on. TPS “as on ‘95 “is 3 one, 515?. 04: S €\\§?\‘CQ W39 QCBOVC. LEAVE Vie») 1? \"‘\ Ox new “SH: (DNA but o\€:C{~I\QA :p‘ we, PPQGQJA ’HAQ, MOBWKX [E F WL‘COM 0325?. PG \\ ‘ \DO'DIHvQ— AQQCnWC“ 0~né> 13V Rf) AQ‘Cif<\\'e. ‘9 905‘ “06 or “13(3le ALQervrC, A 430wa \S ‘mAtfin‘x’rL W 0‘ £of some ._5 two. @ 93% Con Wm 3N2. (x new in‘vgvvrghkn‘on “CDC CD RICA—o Pg V is e.\\§p’t{ (_ P ‘\b \239gbokc. \\ b KLQB>OL=>KLK1>O (DAG) KLKL<O ‘ ‘2, K? ‘5 Aegml‘ce‘ 19 b inAfiRR‘fl 03‘ “PDQ/“’5’ *Uf‘ns‘ 00* +0 \oz 521"“ ALQCnK‘nL, mamims ¥or q\\ in”) 'IXPC§>$O £0“ °~\\ “0 . \ @ Provosx’sion, 11C PeS “5 on e,\\‘\\>*ic. 'Pomx‘) 3 Some. flask bod/“30A V 0‘C \D ‘6. S 50 “MK-\— 0\\\ Voin’ts in \/ bdm 5m We. SWC SEQ. Opg TV"). 3 is: ‘Pes ‘6 cx k3?Q\"\DO\TQ Poinsf; ’vken emu: “Qibkborkooa \/ 0‘? 9 Conan Voirfi‘s on bo’dn 5CAe5 09 11,3“ PFOOC. SoPPoae; ‘\’\V\C&\' P = XLQO) = £03020), Then \ 1. XbNB —. XU U 4, xvv J» EQXW 0&1va um- XWV) \— Emu) . «(0, ) WMU‘L \\W\ u 1 (0,0350 H09!“ Kfl‘NCO‘tfi 1 fig mm V /\\'\2. heicgm’r 09 X050} oqg‘ -‘<\me_ "\5 Swan \ovb A= <x,\\\> = WWW o + <m>v ~r §<<XoooN> 01*3<*W>N>°" *(Kau)H>\l1-' > ’r URN) ~30 \oo5 Tmsbc‘s '“xwv‘em. ') JFm/\<:>Qj\\" Ck“ Q. IQ p is on e,\\§\>’vic Pdij 'eren 11:? i5 Pog‘lfive— 0“ fiasoefidg AQ‘CC‘AGYQ «AA “CU: We. SNML SEA 42)? q\\ :9 P is (x “figu‘bcfix‘g Pogfib amen KP {S Kn Ae-QCAKSVE. 0&5 +016 PFQS‘UW‘ Sirfgfib ‘Cor &‘F€Lre_vx\' \IQGDPS. For .5Mq,\\ moocbk by” 3 U32. Coca IbfiOPQ, onA “mesa obsmq’rions 9mm; M moH: L695 05> quK *0 Oxbubmpsro’x‘k erukiom <=> $907310 . we, see. her a L6 = Co La y La} 15 on «bBMQ‘m’fic. gumL <=> 7. €(U‘5 + (60‘) x- 36131 a TMKS if) Ox For \‘(Q0\o.(‘ QQchnH&\ echqu'QoV/X 520x" QC (,6. Exm?\e_. 00 we -\-oros o? muob’rx‘ofl a: F) 9 =0\ 0‘3?- cos QCCLH‘COS LL\ $0 :5 05\ &&§M?*O*CL Large, g=> 7. VCO‘Y’: cos uCa+<~cos UBLU“) = O or \ U £03237- ——; 3 "‘ Co: LL (0. + rcos 03% .1 wt COM {Dom MS A‘\§Egm\-\‘Q\ qwercm Sow um. (Cm 9‘ ‘02, sowaés wken cos Q>O? > 7 ® (Amer 030005? Vfimdpok AWQLROOS . Rem,“ *chk ogU<3 K5 a \‘me. o? coPVOA'UfK 4:) AMQLU‘JiD - ’MQ oL‘CQ. orfi wadywwum ww\ 3 \ vquafi + amv = xu‘ o» \ ‘ 1 om 0‘ + an)! r ’}\\1 L3 MU\\’:?\~3\\V\¢§ L\\ \03 \I\ <3an ‘03) Q‘) (NRA 50b H‘CLLHAB WU“) we, Sea-V OF LOTDKRC> HAL weinyf 57m QC“) qA’COflfiB <42 E — Q’F3ny 1.- eG’B du‘ CC’SF‘$GBL\I‘3Z:O EXowxp\e. On *ke, —\—oros o? (“mobsn‘ofl’ E: r" F: o G= (macaw so am May e. [V1635 LLQCM- Fuss w} - C(a’vr‘wyfiz] ()‘U‘zo or (WU. r CNH‘Lo‘aLQL (“A ow? r L050}o\1\=0 Or "‘ V (.O\+<‘C,O$Q~\[(l+ WU‘U‘L'O % , “ "‘ \ ‘ 3 \ r > 0";0 Of‘ \I\:O 00c; Nosfke. AeKOA' uskaé‘ we. mm\\.3 r\ CQAQA Hem cook.$ <7) We, obfiemoérmn “\Mofir F=~°=O In—cod') Cooré‘moéte, wNe—b am. “W65 0“: Lof‘ucd-ure, ’? L F=~°=o We. some C)wa 5? edok C0595 oJ‘L insifi‘g (3' Sd‘CqLQS (SC quoblfi‘on. X00 3 < “ (PC‘A €05 LL;CP («\s‘m uL, O) Xw = (- (PICASM wrm Losw, o) Xw = ( CP“ Lv\ cos q, CP“Lu\ sin LL‘@OV“(0\). 50 E = ‘m- F=O. G=(<x>‘>z+cuv‘>7;= lochL. wt osom\\u> assume, he: OLGA "\b poxmdfiltd b3 osflms’rk, so C: = 1. Tkos \ " (Psan 43‘ C05 “\- ‘ q) Loam Q = 2%. Xov X0 X00 .2 a CpcosbL. Q‘sinbL —q)5§r\ LL 0 59‘ o - WWW(«920m .- : —. CW‘. .. (95in UK. Q‘cos, % .. cp‘ 5;“ R \ - I ‘C ; 2?) (X03x031‘003 :— 5 q) LObQL cp‘s‘n q’ (p 035% O q) 0 L— &P‘ (~ QQ‘ sin u. Lobu. - C—V (N)an upcofiwL») —. — L C? -Qs‘mu (P‘cosu. ©“Lobu. \ . u ~ cywomsv— cum (P w 0 q)\ k?“ = -\-— (d k\)‘ (-— CW3;er ~ ‘Pq’ucosch * “We UN” sihzw-CQCP ((5%)) = xv‘cp‘l WP‘. Nostkc M)‘ as §\,\o¢\A \ooK ‘CowachC‘l. From gsoof o\c§ homework he gomq’mce o? 0&8“? =(CPCQ‘W5‘3) W: = \w—w ((Q‘3‘- 0W) 2 K since. C(QAW is unfi weed. Me Know-5 ‘\'\'\03V ’\‘\'\€, (DOPAQACQY‘C CON (5 062, “has <5c CuNOGWPQ; here“ +00: we um come, a? wi‘dn 0» \OQNVU‘ UQVefaf2§0n ‘Qor K. Soxfifle. Woes” (9‘1 * “wt 5 4.) 50 CXKWUEnSYCcQfiN—S w.(‘.\. \J) UJL 36? ac?‘ C?“ * AVA)“ =OX or cp'cfi‘;-u\2‘uv“ Tkos‘ VQNOMJXVKDA M063 COR b¥m¥ (J—Q‘O‘bscoxfi CU‘VOGVUPQ (o \9 (MA oaks {1C3 q)“ = _ KOCQ - @ byzva ofe, “\Me, s§\o\'10v\5 0? 5MB 0.0.5.? K :+/_\_ (9“:‘(9 CPLJ\:5§V\\I 0 £05 \I \PGA :- (.05 \J or sir“, s Ker-O CP : COCA: ON *b ‘ Lofib or‘ (ASWAAEI‘ ( [9&0va \\ 1"P [or-"fl. C9 7' (9613‘ CD229] \ 1* Lol\\ \oz. 0~ \nomzuoor‘é exercisa *0 work 00* a \otw gwmmekdzcfin‘on ’90P *k{5 §0V$cxce Exmfle, $UPC¢LQ5 (Adda are, firoxpks o? £0n€3fions \n (.0913 . XLUN\ = CUNWWONW Q 1V5 Means ’“Ao‘k' 2- a K 3 5133i ; \Wuo‘Aw “‘ kw EC“? UMva ' 1n \Dof*{(.0\ck(‘) we, see. qufr MAC 5%“ 04: \4 {5 03an ‘03 5&2, AeA—ecmx‘mm’? O41 Hm. “665(0wi moéfl‘? x M00 M00 H : \«W m ) 3m\\\v\o> 0: H403? We, \’\€J9&‘mr\ omA “ma. 664.008 S3006. o. Meflsfcxx £06m 052, @L\ak\.e_é\- ’5.“ xmflv 6% on 003 axmdczon '3], .\,\,\e_ beconA éuwo‘kue 059 \n in AMA A§M¥~on ...
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