作者：Wilhelm Klingenberg[
页数：12,178页
出版社：世界图书出版公司北京公司
出版日期：2000
ISBN：9787506200813
电子书格式：pdf/epub/txt
内容简介
Springer数学研究生教材系列之一，深受广大高校师生的欢迎，自从1978年初版至今，不断重印，已经成为经典！微分几何在数学领域中的重要性，已经在数学中的角色不容赘述，为了缓解当前国内在这个领域的燃眉之急，引进了次教材，已经被国内多所院校选作教材。
作者简介
W. Klingenberg ，德国波恩大学数学研究所(MathemaftischesInstitut der Universitat Bonn)教授，著有A Course in Differential Geometry，Lectures on Closed Geodesics ，Lineare Algebra und Geometrie 等多部研究生教材。
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
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
