[按需印刷]曲线与曲面的微分几何（英文版） Manfredo P.Do …|17786 下载 mobi epub pdf 电子书 2024

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店铺：互动出版网图书专营店

出版社：机械工业出版社

ISBN：7111139119

商品编码：25200611079

丛书名：经典原版书库

出版时间：2004-03-01

页数：503

图书描述

书名：	曲线与曲面的微分几何（英文版）[按需印刷]\|17786
图书定价：	110元
图书作者：	Manfredo P.Do Carmo
出版社：	机械工业出版社
出版日期：	2004-03-01 0:00:00
ISBN号：	7111139119
开本：	16开
页数：	503
版次：	1-1

内容简介

本书是一本关于曲线和曲面微分几何的导论，介绍微分几何这两个方面的局部特性与整体特性。同传统的微分几何教材不同，本书更广泛地应用初等线性代数的知识，并把重点放在基本的几何论据上。为取得概念与实际材料之间的适度平衡，本书还包含大量的例子，并合理安排习题，其中包含经典微分几何的某些实际题材。

Some Remarks on Using this Book vii
Curves 1
Introduction I
Parametrized Curves 2
Regular Curves; Arc Length 5
The Vector Product in Ra3 11
The Local Theory of Curves Parametrized by Arc Length 16
The Local Canonical Form 27
Global Properties of Plane Curves 30
Regular Surfaces 51
Introduction 51
Regular Surfaces; Inverse Images of Regular Values 52
Change of Parameters; Differential Functions on Surfaces 69
The Tangent Plane; the Differential of a Map 83
The First Fundamental Form; Area 92
Orientation of Surfaces 102
A Characterization of Compact Orientable Surfaces 109
A Geometric Definition of Area 114
Appendix: A Brief Review on Continuity
and Differentiability 118
3. The Geometry of the Gauss Map 134
3-1 Introduction 134
3-2 The Definition of the Gauss Map and
Its Fundamental Properties 135
3-3 The Gauss Map in Local Coordinates 153
3-4 Vector Fields 175
3-5 Ruled Surfaces and Minimal Surfaces 188
Appendix: Self-Adjoint Linear Maps and Quadratic Forms 214
4. The Intrinsic Geometry of Surfaces 217
4-1 Introduction 217
4-2 Isometries; Conformal Maps 218
4-3 The Gauss Theorem and the Equations of Compatibility 231
4-4 Parallel Transport; Geodesics 238
4-5 The Gauss-Bonnet Theorem and its Applications 264
4-6 The Exponential Map. Geodesic Polar Coordinates 283
4-7 Further Properties of Geodesics. Convex Neighborhoods 298
Appendix: Proofs of the Fundamental Theorems of
The Local Theory of Curves and Surfaces 309
5. Global Differential Geometry 315
5-1 Introduction 315
5-2 The Rigidity of the Sphere 317
5-3 Complete Surfaces. Theorem of Hopf-Rinow 325
5-4 First and Second Variations of the Arc Length;
Bonnet's Theorem 339
5-5 Jacobi Fields and Conjugate Points 357
5-6 Covering Spaces; the Theorems of Hadamard 371
5-7 Global Theorems for Curves; the Fary-Miinor Theorem 380
5-8 Surfaces of Zero Gaussian Curvature 408
5-9 Jacobi's Theorems 415
5-10 Abstract Surfaces; Further Generalizations 425
5-11 Hilbert's Theorem 446
Appendix: Point-Set Topology of Euclidean Spaces 456
Bibliography and Comments 471
Hints and Answers to Some Exercises 475
Index 497

[按需印刷]曲线与曲面的微分几何（英文版） Manfredo P.Do …|17786 下载 mobi epub pdf txt 电子书格式