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米尔诺 (J.Milnor) 著 / 世界图书出版公司 / 2011-07 / 平装
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莫尔斯理论
Thisbookgivesapresent-dayaccountofMarstonMorse'stheoryofthecalculusofvariationsinthelarge.However,therehavebeenIm-portantdevelopmentsduringthepastfewyearswhicharenotmentioned.Letmedescribethreeofthese.
PREFACEPART1NON-DEGENERATESMOOTHFUNCTIONSONAMANIFOLDIntroductionDefinitionsandLenmmsHomotopyTypeinTeRnsofCriticalValuesExamplesTheMorseInequalitiesManifoldsinEuclideanSpace:TheExistenceofNon-degenerateFunctionsTheLefschetzTheoremonHyperplaneSectionsPART2ARAPIDCOURSEINRIEMANNIANGEOMETRYCovariantDifferentiationTheCurvatureTensorGeodesicsandCompletenessPART3THECALCULUSOFVARIATIONSAPPLIEDTOGEODESICSThePathSpaceofaSmoothManifoldTheFnergyofaPathTheHessianoftheEnergyFunctionataCriticalPathJacobiFields:TheNull-spaceofE**TheIndexTheoremAFiniteDimensionalApproximationtoncTheTopologyoftheFullPathSpaceExistenceofNon-conjugatePointsSomeBetweenTopologyandCurvaturePART4APPLICATIONSTOLIEGROUPSANDSYMMEIRICSPACESSymmetricSpacesLieGroupsasSymmetricSpacesWholeManifoldsofMinimalGeodesicsTheBottPeriodicityTheoremfortheUnitaryGroupThePeriodicityTheoremfortheOrthogonalGroupAPPENDIXTHEHOMOTOPYTYPEOFAMONOTONEUNION
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