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內容簡介

　　《微分幾何專題（英文版）》包含瞭陳省身先生有關微分幾何文章的選集以及他在普林斯頓高等研究院的一些講義，大部分未公開齣版或是隻在小範圍內發錶過。陳省身是現代微分幾何之父，《微分幾何專題（英文版）》給讀者展示瞭微分幾何與其他學科如拓撲學和李群聯係的廣闊前景，作者對各個學科聯係的把握非常精準並且正中要點。
　　陳省身曾在《Atiyah選集》的前言中說過：“無論新的東西如何被改進或者精化，但原始的文章總是直接和達要點……”《微分幾何專題（英文版）》對想學習現代微分幾何的初學者非常有價值，也對專傢們重新思考微分幾何有益。

目錄

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
微分幾何專題（英文版） [Topics In Differential Geometry] 下載 mobi epub pdf txt 電子書

評分☆☆☆☆☆

在知識海量的今天,這本書不一定有多高地位;但是能看完也就是一個勝利

評分☆☆☆☆☆

Good

評分☆☆☆☆☆

Good

評分☆☆☆☆☆

還不錯。就是價格變化快，好書。希望看看能有幫助。

評分☆☆☆☆☆

　　我立刻寫信給塞爾先生，請他授權本書的齣版權，塞爾先生也是非常爽快地答應瞭，就是提瞭一個條件，翻譯好瞭之後在齣版前必須將英文版和中文版發給他審讀。英文版他審讀沒有問題，中文版他說會請颱灣的朋友幫忙看，大概想請李文卿教授幫忙吧。

評分☆☆☆☆☆

　　於品和Garving K. Luli花瞭近一年的時間，將本書的法文版翻譯成英文和中文，期間，於品針對書稿中的名詞和證明方式和塞爾先生交流過，塞爾先生都一一作答，但基本意見都是堅持不改，並拿齣瞭諸如 google 搜索數來驗證自己的觀點。真是個固執的老頭兒。

評分☆☆☆☆☆

專著，值得代數相關專業的研究生學習！

評分☆☆☆☆☆

一本現代微分幾何的問題集，感覺讀完需要很長一段時間，因為看不懂。

評分☆☆☆☆☆

質量不錯，還會再來

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