微分几何教程

　　Upon David Hoffman fell the difficult task of transforming the tightly constructed German text into one which would mesh well with the more relaxed format of the Graduate Texts in Mathematics series. There are some elaborations and several new figures have been added. I trust that the merits of the German edition have survived whereas at the same time the efforts of David helped to elucidate the general conception of the Course where we tried to put Geometry before Formalism without giving up mathematical rigour.本书为英文版。

暂缺《微分几何教程》作者简介

Chapter0
CalculusinEuclideanSpace
0.1EuclideanSpace
0.2TheTopologyofEuclideanSpace
0.3DifferentiationinRn
0.4TangentSpace
0.5LocalBehaviorofDifferentiableFunctions(InjectiveandSurjectiveFunctions)
Chapter1
Curves
1.1Definitions
1.2TheFrenetFrame
1.3TheFrenetEquations
1.4PlaneCurves;LocalTheory
1.5SpaceCurves
1.6Exercises
Chapter2
PlaneCurves:GlobalTheory
2.1TheRotationNumber
2.2TheUmlaufsatz
2.3ConvexCurves
2.4ExercisesandSomeFurtherResults
Chapter3
Surfaces:LocalTheory
3.1Definitions
3.2TheFirstFundamentalForm
3.3TheSecondFundamentalForm
3.4CurvesonSurfaces
3.5PrincipalCurvature,GaussCurvature,andMcanCurvature
3.6NormalFormforaSurface,SpecialCoordinates
3.7SpecialSurfaces,DevelopableSurfaces
3.8TheGaussandCodazzi-MainardiEquations
3.9ExercisesandSomeFurtherResults
Chapter4
IntrinsicGeometryofSurfaces:LocalTheory
4.1VectorFieldsandCovariantDifferentiation
4.2ParallelTranslation
4.3Geodesics
4.4SurfacesofConstantCurvature
4.5ExamplesandExercises
Chapter5
Two-dimensionalRiemannianGeometry
5.1LocalRiemannianGeometry
5.2TheTangentBundleandtheExponentialMap
5.3GeodesicPolarCoordinates
5.4JacobiFields
5.5Manifolds
5.6DifferentialForms
5.7ExercisesandSomeFurtherResults
Chapter6
TheGlobalGeometryofSurfaces
6.1SurfacesinEuclideanSpace
6.2Ovaloids
6.3TheGauss-BonnetTheorem
6.4Completeness
6.5ConjugatePointsandCurvature
6.6CurvatureandtheGlobalGeometryofaSurface
6.7ClosedGeodesicsandtheFundamentalGroup
6.8ExercisesandSomeFurtherResults
References
Index
IndexofSymbols