《微分几威但何教程》是2000年世界图书出版公司出版的图书，作者是Wilhelm Klingenberg。
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 Mat视hematics series. 式它病斤There are some elaborations and seve井让济个手列构屋进或ral new fi饭gures have been added. I trust that the merits of the G来自erman edition have survived whereas at the same time the efforts of David helpe360百科d to elucidate the general conception of the Course wher英甚迅介负满训病歌把e we tried to 促适度告告余put Geometry before Formalism without giving up mathematical rigour殖宗客三病右轴们等毫.
本书为英文版。
Chapter 0 Calculus in Euclidean Space
负独围护世巴的片0.1 Euclidean Sp律班志同ace
0.2 The Topology of Euclidean Space
0.场3 Differentiation in Rn
0.4 Tangent Space
0.5 Local Behavior of Differentiable Functions (Injective and Surjective Functions
Chapter 1 Curves
1.1 Definitions
带施阶语古该配度省接1.2 The Frenet Frame
1.3 The Frenet Equations
1.4 Plane C林思纪调规按湖矛单urves; Local Theory
能别充笔林基1.5 Space Curves
试龙部吗某居叶逐化喜 1.6 Exercises
Chapter 2 Plane Curves: Global Theory
2.1 The Rotation Number
2.2 The Umlaufsatz
2.3 Convex Curves
Chapter 3 Surfaces:Local Theory
3.1 Definitions
3.2 The First Fundamental Form
句婷 3.3 The Seco总江房误校混nd Fundamen专育最只tal Form
3.4 Curves on Surfaces
3.5 Principal Curvature,Gauss Curvature,and Mean Curvature
3.6 Normal Form for a Surface,Special Coordinates
3.7 Special Surfaces,Developable Surfaces
3.8 The Gauss and Codazzi-Mainardi Equations
3.9 Exercises and Some Further Results
Chapter 4 Intrinsic Geometry of Surfaces:Local Theory
4.1 Vector Fields and Covariant Differentiation
4.2 Parallel Translation
4.3 Geodesics
4.4 Surfaces of Constant Curvature
4.5 Examples and Exercises
Chapter 5 Two-dimensional Riemannian Genometry
Chapter 6 The Global Geometry of Surfaces
References
Index
Index of Symbols
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