微分几何专题（英文版） [Topics In Differential Geometry] 下载 mobi epub pdf 电子书 2024

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　　《微分几何专题（英文版）》包含了陈省身先生有关微分几何文章的选集以及他在普林斯顿高等研究院的一些讲义，大部分未公开出版或是只在小范围内发表过。陈省身是现代微分几何之父，《微分几何专题（英文版）》给读者展示了微分几何与其他学科如拓扑学和李群联系的广阔前景，作者对各个学科联系的把握非常精准并且正中要点。
　　陈省身曾在《Atiyah选集》的前言中说过：“无论新的东西如何被改进或者精化，但原始的文章总是直接和达要点……”《微分几何专题（英文版）》对想学习现代微分几何的初学者非常有价值，也对专家们重新思考微分几何有益。

目录

1 From Triangles to Manifolds
1．1 Geometry
1．2 Triangles
1．3 Curves in the plane； rotation index and regular homotopy
1．4 Euclidean three-space
1．5 From coordinate spaces to manifolds
1．6 Manifolds； local tools
1．7 Homology
1．8 Vector fields and generalizations
1．9 Elliptic differential equations
1．10 Euler characteristic as a source of global invariants
1．11 Gauge field theory
1．12 Concluding remarks

2 Topics in Differential Geometry
2．1 General notions on differentiable manifolds
2．1．1 Homology and cohomology groups of an abstract complex
2．1．2 Product theory
2．1．3 An example
2．1．4 Algebra of a vector space
2．1．5 Differentiable manifolds
2．1．6 Multiple integrals
2．2 Riemannian manifolds
2．2．1 Riemannian manifolds in Euclidean space
2．2．2 Imbedding and rigidity problems in Euclidean space
2．2．3 Affine connection and absolute differentiation
2．2．4 Riemannian metric
2．2．5 The Gauss-Bonnet formula
2．3 Theory of connections
2．3．1 Resume on fiber bundles
2．3．2 Connections
2．3．3 Local theory of connections； the curvature tensor
2．3．4 The homomorphism h and its independence of connection
2．3．5 The homomorphism h for the universal bundle
2．3．6 The fundamental theorem
2．4 Bundles with the classical groups as structural groups
2．4．1 Homology groups of Grassmann manifolds
2．4．2 Differential forms in Grassmann manifolds
2．4．3 Multiplicative properties of the cohomology ring of a Grassmann manifold
2．4．4 Some applications
2．4．5 Duality theorems
2．4．6 An application to projective differential geometry

3 Curves and Surfaces in Euclidean Space
3．1 Theorem of turning tangents
3．2 The four-vertex theorem
3．3 Isoperimetric inequality for plane curves
3．4 Total curvature of a space curve
3．5 Deformation of a space curve
3．6 The Gauss-Bonnet formula
3．7 Uniqueness theorems of Cohn-Vossen and Minkowski
3．8 Bernstein's theorem on minimal surfaces

4 Minimal Submanifolds in a Riemannian Manifold
4．1 Review of Riemannian geometry
4．2 The first variation
4．3 Minimal submanifolds in Euclidean space
4．4 Minimal surfaces in Euclidean space
4．5 Minimal submanifolds on the sphere
4．6 Laplacian of the second fundamental form
4．7 Inequality of Simons
4．8 The second variation
4．9 Minimal cones in Euclidean space

5 Characteristic Classes and Characteristic Forms
5．1 Stiefel-Whitney and Pontrjagin classes
5．2 Characteristic classes in terms of curvature
5．3 Transgression
5．4 Holomorphic line bundles and the Nevanlinna theory

6 Geometry and Physics
6．1 Euclid
6．2 Geometry and physics
6．3 Groups of transformations
6．4 Riemannian geometry
6．5 Relativity
6．6 Unified field theory
6．7 Weyl's abelian gauge field theory
6．8 Vector bundles
6．9 Why Gauge theory

7 The Geometry of G-Structures
7．1 Introduction
7．2 Riemannian structure
7．3 Connections
7．4 G-structure
7．5 Harmonic forms
7．6 Leaved structure
7．7 Complex structure
7．8 Sheaves
7．9 Characteristic classes
7．10 Riemann-Roch， Hirzebruch， Grothendieck， and Atiyah-Singer Theorems
7．11 Holomorphic mappings of complex analytic manifolds i
7．12 Isometric mappings of Riemannian manifolds
7．13 General theory of G-structures
微分几何专题（英文版） [Topics In Differential Geometry] 下载 mobi epub pdf txt 电子书 格式

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《完全交上的孤立奇点(第2版)(英文版)》的目的是提供给读者复空间奇点尤其是完全交上的奇点的介绍，所需的预备知识为代数几何、解析几何、代数拓扑一些知识、另外还需了解Stein空间的一些结论，可供代数几何、复解析几何和微分分析方面的研究生和相关研究人员参考。

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原来是作者清华授课的讲义。不像想象中那么好

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　　J.P.塞尔先生的《有限群导引》英文版终于出版了。对于塞尔先生读者一定不陌生，他是二十世纪伟大的数学家之一，今年已经是90岁高龄了。维基百科这样写道:对代数拓扑、代数几何和代数数论做出了基础性的贡献。他于1954年获得菲尔兹奖， 2000年获得沃尔夫奖，2003年获得阿贝尔奖。

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