Elie Cartan (1869-1951)

335 Pages·1993·4.642 MB·English

by  M A Akivis, B A Rozenfelʹd

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(Contiinntu heed boaftc hkpi usb lication)
EliCear tan
(1869-1951)
ELICEA RTAN
Apri1l6 8-99M,ya 6 ,1 591
Translatioofn s
MATHEMATICAL
MONOG HS
RAP
Volume 123
EliCear tan
(1869-1951)
M.A.Aki vis
B. RAo.s enfeld
P (1869-1951)
9JIHK A TAH
M.A.A KHBHC
PoseaclieJihA
E.A .
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ABSTRACT.
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Inclubdiebsl iographical references.
ISB0N- 8218-4(5a8c7i-dX- free)
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Contents
Preface
XI
Chap1te.Tr h eL ifea nWdo rokf E. C artan
§1 .1Pa.r ehnotmse' 1
§1 2..S tudaetans tc hoaonaldl ycee 2
§1 3..U nivesrtsuidteyn t 4
§1 4..D octoofSr c ience 6
§1 5..P rofessor 8
§16..A cadiecmian 17
§1 7.. T heC artfaamni ly 24
§18..C artaannd mtahteh etmiacioaftn hswe o rld 27
Chap2t.eL ri Ger ouapnsAd l gebras 33
§21..G roups 33
§2.L2i.ge r osua pnd aLligee bras 37
§23..K illgis'pn aper 42
§2.. C4arttahne'ss is 45
§2.R5o.o otfst hcel asssiimcpaLllige eor ups 46
§2.I6os.m oprhisomfcs o mpsliexm pLligeeor ups 51
§27..R oootfse xceptcioomnpasllie mx pLligeer oups 51
§2.T8h.eC artmaant rices 53
§2.T9h.eW eyglr oups 55
§21..0 TheW eyalffi nger oups 60
§.211.A ssotciiavaena dl teranlagtievber as 63
§21..2 Caarnt'wosr oknsa lgebras 67
§21..3 Lineraerp reseonfts aitmipLolingeesr oups 69
§21..4 Reasli mpLligeer oups 73
§21..5 Iosmoprhisomfrs e sali mpLligeeor ups 78
§21..6 Reducatniqdvu ea sireLdiugecr toiuvpes 82
§21..7 Simple Cghreovuaplsl ey 84
§21..8 Quasigarnolduo posp s 85
vii
CONTENTS
viii
ChaptePrr o3j.e Scptaicvees P raonjdeM cettirviec s 87
§. 31 R.e aslp aces 8 7
§3.C2o.m plsepxa ces 93
§3.Q3u.a tersnpiaocne s 95
§.34O.c tapvlea nes 96
§35..D egenegreaotmee tries 97
§3.E6q.u ivagleeonmte tries 101
§3.M 7ul.t idimegnesnieiorznaalatolif to hnHese stsrea nsfer
principle 170
§3.F8u.n dameenlteamtles n 190
§3.T9h.ed ualittyr iaapnlrdii tnyc iples 131
§31..0 Spacoevsea rl gewbirtahs dzievrios ors 161
§.311Sp.a coevset re npsroord uocfat lsg ebras 181
§31..2 Degenegreaotmee torviearel sg ebras 121
§31..3 Fingietoem etries 132
Chap4t.eL ri Pes euodougparsn d PfaEffi.qautnai ons 152
§.41L.i pes eudogroups 152
§4.T2h.eK ac-Moaoldgye bras 172
§.43P.fa ffi.aenq utaions 192
§.44C.o mlpetienltye gPrfaaffi.balsney stems 103
§.45P.fa ffi.asny stienim nsv olution 123
§.46T.h ea lgeobfer xat eforrimosr 143
§47..A ppalitioconft hteh eoorfsy y stienim nsov lution 153
§.48M.u ltiipnlteeg irnatleisgn,rv aaalnr taisn,id n tegral
geometry 163
§.49D.i fferefonrtmiasan ld Btehtent uim bers 193
§41..0 New metihno dttshh eeoo rfpy a rtdiiaffle reenqtuiaatli1 o24n s
Chap5t.eTr h eM ethoofMd o viFnrga maensDd i efferntial
Geometry 154
§.51M.o vitnrgi hoefd rFar enDeatbr oaunxd 154
§.52M.o vitnegt raahnepdde rnat asopfhD eermeosu lin 174
§.53C.a arntm'osv ifrnagm es 184
§.54T.h ed erivafotrimounlaals 105
§.55T.h es trucetquuraet ions 125
§.56A.p paltiicoofnt shm ee thoofmd o vifrnagm es 135
§57..S omgee omeetxraimcp les 145
§.58M.u ltidimemnasniiofoinlnEad ulsc lisdpeaacne 185
§5.M9i.n immaaln ifolds 106
§51..0 "sIotrsouparicfce s" 126
§.511.D eformaatinpodrn o jetchteiyoo vrfem ultidimensional
manifolds 166
CONTENTS
ix
§51..2 Invarnioarnmta liozfma atniiofonl ds 107
§5 1..3 "Pseudo-cognefoormmeoatlfhr ypye rsurfaces" 147
Chap6t.eR ri emanMnainainfo lSdysm.m etSrpiacc es 17 7
§61..R iemanmnainainfo lds 177
§6.P2s.e uRdioe-manmnainainfo lds 181
§6.P3a.r adliplslealc eomfve enctt ors 181
§6.. R4iemangneioamnei tnar noy rt hogofrnaamle 138
§6.T5h.ep robolefem m beddaRi inge manniani nmtaao n ifold
Euclisdpeaacne 148
§6.R6i.e manmnainainfo sladtysii sn"fgt haex ioomfp lane"1 58
§6.S7y.m metRriiecm ansnpiaacne s 168
§6.H8e.r mistpiaacne ssy mamse stpraicce s 191
§6.E9l.e meonfst ysm metry 139
§61..0 Thei sotgrroopuyap nsod r bits 169
§.611.A bsoloufst yemsm estpraicce s 189
§61..2 Geomeotftr hye Csaurtbagn roups 199
§61..3 TheC artsabunm anifoolfsd ysm mestpraicce s 200
§61..4 Antipmoadnailfo olfsd ysm mestpraicce s 201
§61..5 Orthogsoynsmatsole f fu nctioonsn ysm mestpraicce s 202
§61..6 Unitraerpyr eseonftna ontciooamncpLsti ger oups 204
§61..7 Thet opoogloyf s ymmestpraicce s 207
§61..8 Homloogiaclagle bra 209
Chap7t.eG re neraSlpiazceeds 211
§71.." Affinceo nnecatniWdoe nysl""' mse trmiacn ifolds" 211
§7.. S2pacweist h caoffinnnee ction 212
§7.S3p.a cweista hE uicdleiasno,ti rcao,np mde trciocn nect2i1o5n
§.7.4 Affinceo nnecitnLi iogenr so uapnssd ymmestpraicce s
witahna ffinceo nnection 216
§7.S5p.ca ewsi tahp rojeccotninveec tion 219
§7.. S6pcaewsi tahc onmfoarclo nnection 220
§7.S7p.ca ewsi tahs ymplceocntniecc tion 221
§7.T8h.er elattihveiotryy uannidfi fietedhlt edh eory 222
§7.F9i.n sslpearc es 223
§71..0 Metrsipca ceso nbt ahnseoe tdi oofan r ea 225
§.711.G eneraslpiazcoeevdsea rl gebras 226
§71..2 Theeq uivaplreonbcalene mdG -structures 228
§71..3 Multidinmaewlne bssi o 231
Conclusion 235
DatoefsC aarnt'Lisf aen Adc tivities 239
LiostfP ublicoafEtl iiCoean rtsa n 241