Boothby W An Introduction to Differentiable Manifolds and Riemannian Geometry, Revised 2ed , AP, 2003, 431s _WPCBJ_ djvu

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微分流形与黎曼几何引论  

概述：
《微分流形与黎曼几何引论》这是一本非常好的微分流形入门书。全书从一些基本的微积分知识入手，然后一点点深入概述，主要内容有：流形概述、多变量函数和映射。
《微分流形与黎曼几何引论》微分流形和子流形、流形上的向量场、张量和流形上的张量场、流形上的积分法、黎曼流形上的微分法以及曲率。书后有难度适中的习题。
《微分流形与黎曼几何引论》全书配有很多精美的插图，本书非常适合初学者阅读，可作为数学系、物理系、机械系等理工科高年级本科生和研究生的非常实用教材。
微分流形与黎曼几何引论  目录: 
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
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