- 微分几何教程(英文版)
- - 作者：Wilhelm Klingenberg|责编:刘慧//高蓉
  - 出版社：世界图书出版公司
  - ISBN：9787506200813
  - 出版日期：2000/12/01
  - 页数：178
- 售价：14.4

内容大纲
本书主要讲述曲面和曲线的经典微分几何学，重点在二维黎曼几何方面。全书在风格上深受陈省身《微分几何讲义》（1954年）一书的影响，论述清晰、严谨、透彻。
作者介绍
目录
Chapter 0  Calculus in Euclidean Space
  0.1  Euclidean Space
  0.2  The Topology of Euclidean Space
  0.3  Differentiation in Rn
  0.4  Tangent Space
  0.5  Local Behavior of Differentiable Functions (Injective and Surjective Functions)
Chapter 1  Curves
  1.1  Definitions
  1.2  The Frenet Frame
  1.3  The Frenet Equations
  1.4  Plane Curves; Local Theory
  1.5  Space Curves
  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
  3.3  The Second Fundamental 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

内容大纲

作者介绍

目录

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