几何．6，黎曼几何

Preface

Chapter1.AffineConnections

1.ConnectiononaManifold

2.CovariantDifferentiationandParallelTranslationAlongaCurve

3.Geodesics

4.ExponentialMappingandNormalNeighborhoods

5.WhiteheadTheorem

6.NormalConvexNeighborhoods

7.ExistenceofLerayCoverings

Chapter2.CovariantDifferentiation.Curvature

Chapter3.AffineMappings.Submanifolds

Chapter4.StructuralEquations.LocalSymmetries

Chapter5.SymmetricSpaces

Chapter6.ConnectionsonLieGroups

Chapter7.LieFunctor

Chapter8.AffineFieldsandRelatedTopics

Chapter9.CartanTheorem

Chapter10.PalaisandKobayashiTheorems

Chapter11.LagrangiansinRiemannianSpaces

Chapter12.MetricPropertiesofGeodesics

Chapter13.HarmonicFunctionalsandRelatedTopics

Chapter14.MinimalSurfaces

Chapter15.CurvatureinRiemannianSpace

Chapter16.GaussianCurvature

Chapter17.SomeSpecialTensors

Chapter18.SurfaceswithConformalStructure

Chapter19.MappingsandSubmanifoldsⅠ

Chapter20.SubmanifoldsⅡ

Chapter21.FundamentalFormsofaHypersurface

Chapter22.SpacesofConstantCurvature

Chapter23.SpaceForms

Chapter24.Four-DimensionalManifolds

Chapter25.MetricsonaLieGroupⅠ

Chapter26.MetricsonaLieGroupⅡ

Chapter27.JacobiTheory

Chapter28.SomeAdditionalTheoremsⅠ

Chapter29.SomeAdditionalTheoremsⅡ

Chapter30.SmoothManifolds

Chapter31.TangentVectors

Chapter32.SubmanifoldsofaSmoothManifold

Chapter33.VectorandTensorFieldsDifferentialForms

Chapter34.VectorBundles

Chapter35.ConnectionsonVectorBundles

Chapter36.CurvatureTensor

SuggestedReading

Index

　　本书为《国外数学名著系列》丛书之一。该丛书是科学出版社组织学术界多位知名院士、专家精心筛选出来的一批基础理论类数学著作，读者对象面向数学系高年级本科生、研究生及从事数学专业理论研究的科研工作者。本册为《几何(Ⅵ黎曼几何影印版)60》。　　ThisbooktreatsthatpartofRiemanniangeometryrelatedtomoreclassicaltopicsinaveryoriginal，clearandsolidstyle.BeforegoingtoRiemanniangeometry，theauthorpresentsamoregeneraltheoryofmanifoldswithalinearconnection.HavinginminddifferentgeneralizationsofRiemannianmanifolds，itisclearlystressedwhichnotionsandtheoremsbelongtoRiemanniangeometryandwhichofthemareofamoregeneralnature.Muchattentionispaidtotransformationgroupsofsmoothmanifolds.　　Throughoutthebook，differentaspectsofsymmetricspacesaretreated.Theauthorsuccessfullycombinestheco-ordinateandinvariantapproachestodifferentialgeometry，whichgivethereadertoolsforpracticalcalculationsaswellasatheoreticalunderstandingofthesubject.Thebookcontainsaveryusefullargeappendixonfoundationsofdifferentiablemanifoldsandbasicstructuresonthemwhichmakesitself-containedandpracticallyindependentfromothersources.　　Theresultsarewellpresentedandusefulforstudentsinmathematicsandtheoreticalphysics，andforexpertsinthesefields.Thebookcanserveasatextbookforstudentsdoinggeometry，aswellasareferencebookforprofessionalmathematiciansandphysicists.