莫尔斯理论

图书标准信息

• 作者 米尔诺（J.Milnor） 著
• 出版社 世界图书出版公司
• 出版时间 2011-07
• 版次 1
• ISBN 9787510037481
• 定价 29.00元
• 装帧 平装
• 开本 24开
• 纸张 其他
• 页数 153页
• 正文语种 英语

【内容简介】

Thisbookgivesapresent-dayaccountofMarstonMorse'stheoryofthecalculusofvariationsinthelarge.However,therehavebeenIm-portantdevelopmentsduringthepastfewyearswhicharenotmentioned.Letmedescribethreeofthese.

【目录】

PREFACE
PART1NON-DEGENERATESMOOTHFUNCTIONSONAMANIFOLD
Introduction
DefinitionsandLenmms
HomotopyTypeinTeRnsofCriticalValues
Examples
TheMorseInequalities
ManifoldsinEuclideanSpace:TheExistenceofNon-degenerateFunctions
TheLefschetzTheoremonHyperplaneSections

PART2ARAPIDCOURSEINRIEMANNIANGEOMETRY
CovariantDifferentiation
TheCurvatureTensor
GeodesicsandCompleteness

PART3THECALCULUSOFVARIATIONSAPPLIEDTOGEODESICS
ThePathSpaceofaSmoothManifold
TheFnergyofaPath
TheHessianoftheEnergyFunctionataCriticalPath
JacobiFields:TheNull-spaceofE**
TheIndexTheorem
AFiniteDimensionalApproximationtonc
TheTopologyoftheFullPathSpace
ExistenceofNon-conjugatePoints
SomeBetweenTopologyandCurvature

PART4APPLICATIONSTOLIEGROUPSANDSYMMEIRICSPACES
SymmetricSpaces
LieGroupsasSymmetricSpaces
WholeManifoldsofMinimalGeodesics
TheBottPeriodicityTheoremfortheUnitaryGroup
ThePeriodicityTheoremfortheOrthogonalGroup
APPENDIXTHEHOMOTOPYTYPEOFAMONOTONEUNION