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

ISBN：

978-7-04-059315-0

版面字数：

703.000千字

开本：

特殊

全书页数：

暂无

装帧形式：

精装

重点项目：

暂无

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

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