微分几何与积分几何
￥ 62.83 8.0折 ￥ 79 九五品
仅1件
作者陈省身
出版社高等教育出版社
ISBN9787040465181
出版时间2016-10
版次1
装帧精装
开本16开
纸张胶版纸
页数246页
字数99999千字
定价79元
上书时间2024-05-28
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基本信息
书名:微分几何与积分几何
定价：79.00元
作者:陈省身
出版社：高等教育出版社
出版日期：2016-10-05
ISBN：9787040465181
字数：310000
页码：246
版次：1
装帧：精装
开本：16开
商品重量：
编辑推荐
《微分几何与积分几何(英文版)》由高等教育出版社出版。
内容提要
《微分几何与积分几何(英文版)》分为四部分：Part Ⅰ What is Geometry and Differential Geometry；Part Ⅱ Lectures on Integral Geometry；Part Ⅲ Differentiable Manifolds；Part Ⅳ Lecture Notes on Differentiable Geometry。《微分几何与积分几何(英文版)》内容包括：What Is Geometry；Lectures on Integral Geometry；Multilinear Algebra；Differentiable Manifolds；Exterior Differential Forms；Affine Connections；Riemannian Manifolds；Review of Surface Theory；Minimal Surfaces；Pseudospherical Surface等。
目录
Part Ⅰ What is Geometry and Differential Geometry 1 What Is Geometry？ 1.1 Geometry as a logical system； Euclid 1.2 Coordinatization of space； Descartes 1.3 Space based on the group concept； Klein's Erlanger Programm 1.4 Localization of geometry； Gauss and Riemann 1.5 Globalization； topology 1.6 Connections in a fiber bundle； Elie Cartan 1.7 An application to biology 1.8 Conclusion 2 Differential Geometry； Its Past and Its Future 2.1 Introduction 2.2 The development of some fundamental notions and tools 2.3 Formulation of some problems with discussion of related results 2.3.1 Riemannian manifolds whose sectional curvatures keep a constant sign 2.3.2 Euler—Poincare characteristic 2.3.3 Minimal submanifolds 2.3.4 Isometric mappings 2.3.5 Holomorphic mappings Part Ⅱ Lectures on Integral Geometry 3 Lectures on Integral Geometry 3.1 Lecture Ⅰ 3.1.1 Buffon's needle problem 3.1.2 Bertrand's parabox 3.2 Lecture Ⅱ 3.3 Lecture Ⅲ 3.4 Lecture Ⅳ 3.5 Lecture Ⅴ 3.6 Lecture Ⅵ 3.7 Lecture Ⅶ 3.8 Lecture Ⅷ Part Ⅲ Differentiable Manifolds 4 Multilinear Algebra 4.1 The tensor （or Kronecker） product 4.2 Tensor spaces 4.3 Symmetry and skew—symmetry； Exterior algebra 4.4 Duality in exterior algebra 4.5 Inner product 5 Differentiable Manifolds 5.1 Definition of a differentiable manifold 5.2 Tangent space 5.3 Tensor bundles 5.4 Submanifolds； Imbedding of compact manifolds 6 Exterior Differential Forms 6.1 Exterior differentiation 6.2 Differential systems； Frobenius's theorem 6.3 Derivations and anti—derivations 6.4 Infinitesimal transformation 6.5 Integration of differential forms 6.6 Formula of Stokes 7 Affine Connections 7.1 Definition of an affine connection： covariant differential 7.2 The principal bundle 7.3 Groups of holonomy 7.4 Affine normal coordinates 8 Riemannian Manifolds 8.1 The parallelism of Levi—Civita 8.2 Sectional curvature 8.3 Normal coordinates； Estence of convex neiourhoods 8.4 Gauss—Bonnet formula 8.5 Completeness 8.6 Manifolds of constant curvature Part Ⅳ Lecture Notes on Differentiable Geometry 9 Review of Surface Theory 9.1 Introduction 9.2 Moving frames 9.3 The connection form 9.4 The complex structure 10 Minimal Surfaces 10.1 General theorems 10.2 Examples 10.3 Bernstein —Osserrnan theorem 10.4 Inequality on Gaussian curvature 11 Pseudospherical Surface 11.1 General theorems 11.2 Backlund's theorem
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