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微分几何教程 英文版PDF|Epub|txt|kindle电子书版本下载
- （德）Wilhelm Klingenberg著 著
- 出版社： 世界图书出版公司北京公司
- ISBN：7506200813
- 出版时间：2000
- 标注页数：180页
- 文件大小：23MB
- 文件页数：189页
- 主题词：
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图书目录
Chapter 0 Calculus in Euclidean Space1
0.1 Euclidean Space1
0.2 The Topology of Euclidean Space2
0.3 Differentiation in Rn3
0.4 Tangent Space5
0.5 Local Behavior of Differentiable Functions（Injective and Surjective Functions）6
Chapter 1 Curves8
1.1 Definitions8
1.2 The Frenet Frame10
1.3 The Frenet Equations11
1.4 Plane Curves;Local Theory15
1.5 Space Curves17
1.6 Exercises20
Chapter 2 Plane Curves;Global Theory21
2.1 The Rotation Number21
2.2 The Umlaufsatz24
2.3 Convex Curves27
2.4 Exercises and Some Further Results29
Chapter 3 Surfaces：Local Theory33
3.1 Definitions33
3.2 The First Fundamental Form35
3.3 The Second Fundamental Form38
3.4 Curves on Surfaces43
3.5 Principal Curvature,Gauss Curvature,and Mean Curvature45
3.6 Normal Form for a Surface,Special Coordinates49
3.7 Special Surfaces,Developable Surfaces54
3.8 The Gauss and Codazzi-Mainardi Equations61
3.9 Exercises and Some Further Results66
Chapter 4 Intrinsic Geometry of Surfaces：Local Theory73
4.1 Vector Fields and Covariant Differentiation74
4.2 Parallel Translation76
4.3 Geodesics78
4.4 Surfaces of Constant Curvature83
4.5 Examples and Exercises87
Chapter 5 Two-dimensional Riemannian Geometry89
5.1 Local Riemannian Geometry90
5.2 The Tangent Bundle and the Exponential Map95
5.3 Geodesic Polar Coordinates99
5.4 Jacobi Fields102
5.5 Manifolds105
5.6 Differential Forms111
5.7 Exercises and Some Further Results119
Chapter 6 The Global Geometry of Surfaces123
6.1 Surfaces in Euclidean Space123
6.2 Ovaloids129
6.3 The Gauss-Bonnet Theorem138
6.4 Completeness144
6.5 Conjugate Points and Curvature148
6.6 Curvature and the Global Geometry of a Surface152
6.7 Closed Geodesics and the Fundamental Group156
6.8 Exercises and Some Further Results161
References167
Index171
Index of Symbols177