资源描述：
《foundations of differential geometry vol 1 - kobayashi, nomizu》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、-.,..-,A'&-*:+"2FOUN@ATIOkSY_*.,.;y1*:.,ijI;,:OFDIFlf’ERENl%.ALNumber15,vol,...e:>&?a~:GEOMETRY’’FOUNDATIONS.OFDIFFAER$NTI&GE&ETRYByShoshichiKobayashi6adKabumi~No&znTr..,.a-‘.,.VOLUMEI_SHOSHICHIKOBAYASHIUniversityofCalifornia,Berkeley,CaliforniaandKATSUMINOMIZUBrownUnive
2、rsity,Providence,RhodeIslandt1963:?I,INTERSCIENCEPUBLISHERSn.,INTER8CIENCEPUBLISHEqSadi~is&nzfJohnWilbyiSo&,NewYorki“-Londonadl~isionof.i&Wiley&Sons,NewYork+*s-.PREFACEDifferentialg&etryhasalongl&dryasa&ldofmathematicsandyetitsrigorousfoundaticvnin”&erealmofcontemporaryma
3、thematicsis:nlativelynew.Weh&writtenthisbook,thefirstofthetwe;ivolumesoftheFdatiwdfD@nntialGeometry,withtheintitionofprovid&a”lv&&ticintroductiontodifferential‘&ometryw&h@also,&ve’‘a~areferencebook.Ourprimaryconce~wastomakeit,+l&&ta.@edasmuchaspossibleandtogivecompl&~MO&o
4、fali’&d&dresultsinthefoundation.Wehopethat;&&pwhasbeen$chievedwiththefollowingarrangtments.InchapterIwehavegivenabriefsurvq;ofdifferentiableim&nKMs,,I$&mtipsAd,fibrebundles.Thereaderswho-areu&amil&G&h&din.,qaylearnthisubjectsfromt+ebooks+fChevotlley,ppin,Pontrjagin,andSte
5、enrod,listedintheBilkaieourstandardreferencesinChapterI.Weacoficiseaccountoftensor-algti&dMU&fiek&th&“&n<hemeofwhichisthenotiib;ief8~h’aFtihc‘k&ebr&oftensOrfields.IntheAppdiccs,wehave@Gnsome‘r&t&sfromtopology,Liegrbuptheoryandothirswhich%ven’eed&.theiaintext.Withthesepr
6、eparations,themaint&tofthibookis&l&ontained.ChapterII-c&ntains&econilectiontheoryofEhresmannanditslateqdevelopment.ResultsinthischapterareappliedtolinearandaffifiecdnnectionsinChapterIIIatidtoRiemannianconnectionsinChapterIV.Mat~ybasicresultsonnormalcoordinates,convexneig
7、hborhoods,dis!ance,cotipletenessandMonomygroupsare’p&&lherecompletely,includingthedi:RhamdecompositionthearemforRi&mannianm&lds;‘I-InChhpterv,-we‘int&&cethesectionalcurvatureof’aRiemelM%&Id.‘a&itbtSpacesofconstantcurvattire.AmorecompletetreMment!&“&$ert&ofRiemanni&manifol
8、dsinvolvingHctional‘&&+attrSdependson“talculusofiariationsandwilltiegivenII.We’discussflat’affin
