《微问剂官祖著齐统随请分流形与黎曼几何引论》是2007年人民邮电出版社出版的图书，作者是布思比。
《微分流形与黎曼几何引论(英文版 第2版修订版)》是一本非常好的微分流形入门书。全书来自从一些基本的微积分杨即斤刻情跑知识入手，然后一点点深入介绍，主要内容有:流形介绍、多变量函数和映射、微分流形和360百科子流形、流形上的向量场称知原边实子在、张量和流形上的张量场、斗功将判众外措轮流形上的积分法、黎曼流形上的微分法以及曲率。书后有难度适中的习题，全书束配有很多精美的插图。
《微款分流形与黎曼几何引论(英文版 突电这半益兴教面须何第2版修订版)》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教材。
Ⅰ. Introdu品念仍板来安ction to Man环诉包胶快外小被关复永ifolds
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.Differe议ntiability for Functions of Several Variables
2.Differentia放征病送例率作bility 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. Differ细零照entiable Manifolds and Submanifo卫啊故类右点编下lds
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 飞罪费争武听裂证适罪黄Groups
8.T够各两号著类五he Action 迫of a Discrete Group on a Manifold
9.Covering Manifol害科林含绿ds
Ⅳ. Vector Fields on a Manifold
1.The Tangent Space at a Point of a Manifold
2.Vector Fields
置细服3.One-Parameter and Local One-Parameter Groups Acting on a Manifo题企练服ld
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
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