微分几何: 曲线、曲面和流形（第三版）（影印版）

样章

作者：

Wolfgang Kühnel, Translated by Bruce Hunt

定价：

169.00 元

版面字数：

703千字

开本：

特殊

装帧形式：

精装

版次：

最新版次
印刷时间：

2023年

ISBN：

978-7-04-059315-0

物料号：

59315-00

出版时间：

2023-03-15

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

几何学

暂无

目录
- 前辅文
- Chapter 1. Notations and Prerequisites from Analysis
- Chapter 2. Curves in IRn
  - 2A Frenet curves in IRn
  - 2B Plane curves and space curves
  - 2C Relations between the curvature and the torsion
  - 2D The Frenet equations and the fundamental theorem of the
  - local theory of curves
  - 2E Curves in Minkowski space IR
  - 2F The global theory of curves
  - Exercises
- Chapter 3. The Local Theory of Surfaces
  - 3A Surface elements and the first fundamental form
  - 3B The Gauss map and the curvature of surfaces
  - 3C Surfaces of rotation and ruled surfaces
  - 3D Minimal surfaces
  - 3E Surfaces in Minkowski space IR
  - 3F Hypersurfaces in IRn+1
  - Exercises
- Chapter 4. The Intrinsic Geometry of Surfaces
  - 4A The covariant derivative
  - 4B Parallel displacement and geodesics
  - 4C The Gauss equation and the Theorema Egregium
  - 4D The fundamental theorem of the local theory of surfaces
  - 4E The Gaussian curvature in special parameters
  - 4F The Gauss-Bonnet Theorem
  - 4G Selected topics in the global theory of surfaces
  - Exercises
- Chapter 5. Riemannian Manifolds
  - 5A The notion of a manifold
  - 5B The tangent space
  - 5C Riemannian metrics
  - 5D The Riemannian connection
- Chapter 6. The Curvature Tensor
  - 6A Tensors
  - 6B The sectional curvature
  - 6C The Ricci tensor and the Einstein tensor
- Chapter 7. Spaces of Constant Curvature
  - 7A Hyperbolic space
  - 7B Geodesics and Jacobi fields
  - 7C The space form problem
  - 7D Three-dimensional Euclidean and spherical space forms
  - Exercises
- Chapter 8. Einstein Spaces
  - 8A The variation of the Hilbert-Einstein functional
  - 8B The Einstein field equations
  - 8C Homogenous Einstein spaces
  - 8D The decomposition of the curvature tensor
  - 8E The Weyl tensor
  - 8F Duality for four-manifolds and Petrov types
  - Exercises
- Solutions to selected exercises
- Bibliography
- List of notation
- Index