《微分流形與黎曼幾何引論》是2007年人民郵電出版社出版的圖書，作者是布思比。
基本介紹
- 書名：微分流形與黎曼幾何引論
- 作者：布思比
- ISBN：9787115165992
- 頁數：419
- 定價：59.00元
- 出版社：人民郵電出版社
- 出版時間：2007-9
- 叢書： 圖靈原版數學·統計學系列
內容簡介,圖書目錄,
內容簡介
《微分流形與黎曼幾何引論(英文版 第2版修訂版)》是一本非常好的微分流形入門書。全書從一些基本的微積分知識入手，然後一點點深入介紹，主要內容有：流形介紹、多變數函式和映射、微分流形和子流形、流形上的向量場、張量和流形上的張量場、流形上的積分法、黎曼流形上的微分法以及曲率。書後有難度適中的習題，全書配有很多精美的插圖。
《微分流形與黎曼幾何引論(英文版 第2版修訂版)》非常適合初學者閱讀，可作為數學系、物理系、機械系等理工科高年級本科生和研究生的教材。
圖書目錄
Ⅰ. Introduction to Manifolds
1.Preliminary Comments on Rn
2.Rn and Euclidean Space
3.Topological Manifolds
4.Further Examples of Manifolds. Cutting and Pasting
5.Abstract Manifolds. Some Examples
Ⅱ. Functions of Several Variables and Mappings
1.Differentiability for Functions of Several Variables
2.Differentiability of Mappings and Jacobians
3.The Space of Tangent Vectors at a Point of Rn
4.Another Definition of Ta(Rn)
5.Vector Fields on Open Subsets of Rn
6.The Inverse Function Theorem
7.The Rank of a Mapping
Ⅲ. Differentiable Manifolds and Submanifolds
1.The Definition of a Differentiable Manifold
2.Further Examples
3.Differentiable Functions and Mappings
4.Rank of a Mapping, Immersions
5.Submanifolds
6.Lie Groups
7.The Action of a Lie Group on a Manifold. Transformation Groups
8.The Action of a Discrete Group on a Manifold
9.Covering Manifolds
Ⅳ. Vector Fields on a Manifold
1.The Tangent Space at a Point of a Manifold
2.Vector Fields
3.One-Parameter and Local One-Parameter Groups Acting on a Manifold
4.The Existence Theorem for Ordinary Differential Equations
5.Some Examples of One-Parameter Groups Acting on a Manifold
6.One-Parameter Subgroups of Lie Groups
7.The Lie Algebra of Vector Fields on a Manifold
8.Frobenius's Theorem
9.Homogeneous Spaces
Ⅴ. Tensors and Tensor Fields on Manifolds
1.Tangent Covectors
2.Bilinear Forms. The Riemannian Metric
3.Riemannian Manifolds as Metric Spaces
4.Partitions of Unity
5.Tensor Fields
6.Multiplication of Tensors
7.Orientation of Manifolds and the Volume Element
8.Exterior Differentiation
Ⅵ. Integration on Manifolds
Ⅶ. Differentiation on Riemannian Manifolds
Ⅷ. Curvature
REFERENCES
INDEX
1.Preliminary Comments on Rn
2.Rn and Euclidean Space
3.Topological Manifolds
4.Further Examples of Manifolds. Cutting and Pasting
5.Abstract Manifolds. Some Examples
Ⅱ. Functions of Several Variables and Mappings
1.Differentiability for Functions of Several Variables
2.Differentiability of Mappings and Jacobians
3.The Space of Tangent Vectors at a Point of Rn
4.Another Definition of Ta(Rn)
5.Vector Fields on Open Subsets of Rn
6.The Inverse Function Theorem
7.The Rank of a Mapping
Ⅲ. Differentiable Manifolds and Submanifolds
1.The Definition of a Differentiable Manifold
2.Further Examples
3.Differentiable Functions and Mappings
4.Rank of a Mapping, Immersions
5.Submanifolds
6.Lie Groups
7.The Action of a Lie Group on a Manifold. Transformation Groups
8.The Action of a Discrete Group on a Manifold
9.Covering Manifolds
Ⅳ. Vector Fields on a Manifold
1.The Tangent Space at a Point of a Manifold
2.Vector Fields
3.One-Parameter and Local One-Parameter Groups Acting on a Manifold
4.The Existence Theorem for Ordinary Differential Equations
5.Some Examples of One-Parameter Groups Acting on a Manifold
6.One-Parameter Subgroups of Lie Groups
7.The Lie Algebra of Vector Fields on a Manifold
8.Frobenius's Theorem
9.Homogeneous Spaces
Ⅴ. Tensors and Tensor Fields on Manifolds
1.Tangent Covectors
2.Bilinear Forms. The Riemannian Metric
3.Riemannian Manifolds as Metric Spaces
4.Partitions of Unity
5.Tensor Fields
6.Multiplication of Tensors
7.Orientation of Manifolds and the Volume Element
8.Exterior Differentiation
Ⅵ. Integration on Manifolds
Ⅶ. Differentiation on Riemannian Manifolds
Ⅷ. Curvature
REFERENCES
INDEX
