点击选择搜索分类
首页 - 技法/教程- 正文
☆☆☆☆☆
||
Shiing-Shen Chen 编
出版社: 高等教育出版社 ISBN:9787040465174 版次:1 商品编码:12062328 包装:精装 外文名称:Topics In Differential Geometry 开本:16开 出版时间:2016-10-01 用纸:胶版纸 页数:225 字数:290000 正文语种:英文
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。
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] 电子书 下载 mobi epub pdf txt
微分几何专题(英文版) [Topics In Differential Geometry]-so88
微分几何专题(英文版) [Topics In Differential Geometry] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
Shiing-Shen Chen 编
出版社: 高等教育出版社 ISBN:9787040465174 版次:1 商品编码:12062328 包装:精装 外文名称:Topics In Differential Geometry 开本:16开 出版时间:2016-10-01 用纸:胶版纸 页数:225 字数:290000 正文语种:英文
内容简介
《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 Manifolds1.1 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] 电子书 下载 mobi epub pdf txt
电子书下载地址:
相关电子书推荐:
- 文件名
- 半知一解:世界经典趣味哲学 9787549624607
- 让步,才会更进步
- 天机:大西国揭秘 第四部 燃烧的星空 9787515820378 叶远-RT
- 左手幸福右手贞操
- 空想科学理科读本
- 恋爱要懂点催眠术 9787545408737
- 地理之 9787222153448
- 纳米科学与技术:微纳加工及在纳米材料与器件研究中的应用
- 中侨大讲堂:中外人文大讲堂 9787511365101 周曲,刘凤珍-RT
- 原子和量子物理学(第7版)
- 植物生长2(英语科普阅读系列)
- 你不可不知的50个数学知识
- 宇宙之美 9787559609410 [法]雅克保罗 [法]让-吕克罗贝尔-艾斯尔-RT
- 中外物理学精品书系·引进系列(13)·等离子体天体物理学(第1部分):原理与实践(影印版) [Plasma Astrophysics,Part I:Fundamentals and Practice]
- 彩色口袋自然珍藏图鉴 花朵(全彩)