微分幾何專題（英文版） [Topics In Differential Geometry] pdf epub mobi txt 电子书 下载 2025

☆☆☆☆☆

Shiing-Shen Chen 編

齣版社： 高等教育齣版社

ISBN：9787040465174

版次：1

商品編碼：12062328

包裝：精裝

外文名稱：Topics In Differential Geometry

開本：16開

齣版時間：2016-10-01

用紙：膠版紙

頁數：225

字數：290000

正文語種：英文

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

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據說GSM將會印全套，就像GTM一樣慢慢地全有瞭

评分☆☆☆☆☆

有限群的書，不錯的，嘿嘿

评分☆☆☆☆☆

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

评分☆☆☆☆☆

書的質量不錯，印刷也很清晰

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　　“藝術傢的優良品質，無非是智慧、專心、真摯、意誌。像一個誠實的工人一樣完成你們的工作吧。”丘成桐教授特意在《數學的藝術》中提到這段羅丹的遺囑，他認為藝術傢和科學傢有著同樣的目標。小編在與塞爾先生因《有限群導引》一書打交道的過程中，深刻地體會到瞭布爾巴基學派所具備治學嚴謹、對一部著作要經過反復修改,直到滿意為止的優良傳統。

评分☆☆☆☆☆

　　“藝術傢的優良品質，無非是智慧、專心、真摯、意誌。像一個誠實的工人一樣完成你們的工作吧。”丘成桐教授特意在《數學的藝術》中提到這段羅丹的遺囑，他認為藝術傢和科學傢有著同樣的目標。小編在與塞爾先生因《有限群導引》一書打交道的過程中，深刻地體會到瞭布爾巴基學派所具備治學嚴謹、對一部著作要經過反復修改,直到滿意為止的優良傳統。

评分☆☆☆☆☆

質量不錯，還會再來

评分☆☆☆☆☆

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