黎曼-芬斯勒几何导论 An Introduction to Riemann-Finsler Geometry 英文版[DJVU]

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资源信息： 中文名: 黎曼-芬斯勒几何导论 原名: An Introduction to Riemann-Finsler Geometry 作者: 鲍大维 陈省身 沈忠民 李养成 郭瑞芝 崔登兰 Akbar-Zadeh 图书分类: 科技 资源格式: DJVU 版本: 英文版 出版社: 世界图书出版公司 书号: 9787510005053 发行时间: 2009年 地区: 大陆 语言: 英文 概述:

书名： An Introduction to Riemann-Finsler Geometry (GTM 200) 中译名： 黎曼-芬斯勒几何导论 作者： D. Bao, S-S. Chern, Z.Shen 世图书号： WB0505 原版书号： 978-7-5100-0505-3 定价： ¥50.00 元 原出版社： Springer 原版出版年代： 2000 世图影印年代： 2009 扫描分辨率: 600 dpi , 455 Scans djvu 阅读器： http://windjview.sourceforge.net/ 本书的作者之一是已故数学大师陈省身，全书分为3部分，全面介绍了黎曼-芬斯勒几何的基本概念和最新研究成果。 目次：（一）芬斯勒流形及其曲率：芬斯勒流形和闵可夫斯基范数基础知识；陈氏联络；曲率和舒尔引理；芬斯勒曲面和广义高斯-博内定理。（二）变分计算和比较定理：弧长变分、雅可比场和曲率效应。高斯引理和Hopf-Rinow定理；索引式和Bonnet-Myers定理；剖分、共轭轨迹和Synge’s定理；Cartan- Hadamard定理和 Rauch第一定理。（三）特殊芬斯勒空间：Berwald空间和Szabo定理；Rander空间和Elegant定理；常数标志曲率空间和 Akbar-Zadeh定理；曼流形和Hopf定理；闵可夫斯基空间及Deicke 和Brickell定理。

目录: Preface Acknowledgments PART ONE Finsler Manifolds and Their Curvature CHAPTER 1 Finsler Manifolds and the Fundamentals of Minkowski Norms 1.0 Physical Motivations 1.1 Finsler Structures: Definitions and Conventions 1.2 Two Basic Properties of Minkowski Norms 1.2 A. Euler's Theorem !, 1.2 B. A Fundamental Inequality 1.2 C. Interpretations of the Fundamental Inequality 1.3 Explicit Examples of Finsler Manifolds 1.3 A. Minkowski and Locally Minkowski Spaces 1.3 B. Riemannian Manifolds 1.3 C. Randers Spaces 1.3 D. Berwald Spaces 1.3 E. Finsler Spaces of Constant Flag Curvature 1.4 The Fundamental Tensor and the Cartan Tensor References for Chapter 1 CHAPTER 2 The Chern Connection 2.0 Prologue 2.1 The Vector Bundle TM and Related Objects 2.2 Coordinate Bases Versus Special Orthonormal Bases 2.3 The Nonlinear Connection on the Manifold TM 2.4 The Chern Connection on TM 2.5 Index Gymnastics References for Chapter 2 CHAPTER 3 Curvature and Schur's Lemma 3.1 Conventions and the hh-, hv-, w-curvatures 3.2 First Bianchi Identities from Torsion Freeness 3.3 Formulas for R and P in Natural Coordinates 3.4 First Bianchi Identities from "Almost" g-compatibility 3.5 Second Bianchi Identities 3.6 Interchange Formulas or Ricci Identities 3.7 Lie Brackets among the and the 3.8 Derivatives of the Geodesic Spray Coefficients Gi 3.9 The Flag Curvature 3.10 Schur's Lemma References for Chapter 3 CHAPTER 4 Finsler Surfaces and a Generalized Gauss-Bonnet Theorem 4.0 Prologue 4.1 Minkowski Planes and a Useful Basis 4.2 The Equivalence Problem for Minkowski Planes 4.3 The Berwald Frame and Our Geometrical Setup On SM 4.4 The Chern Connection and the Invariants I, J, K 4.5 The Riemannian Arc Length of the Indicatrix 4.6 A Gauss-Bonnet Theorem for Landsberg Surfaces References for Chapter 4 PART TWO Calculus of Variations and Comparison Theorems CHAPTER 5 Variations of Arc Length, CHAPTER 6 The Gauss Lemma and the Hopf-Rinow Theorem CHAPTER 7 The Index Form and the Bonnet-Myers Theorem CHAPTER 8 The Cut and Conjugate Loci, and Synge's Theorem CHAPTER 9 The Cartan-Hadamard Theorem and Rauch's First Theorem PART THREE Special Finsler Spaces over the Reals CHAPTER 10 Berwald Spaces and Szab6's Theorem for Berwald Surfaces CHAPTER 11 Randers Spaces and an Elegant Theorem CHAPTER 12 Constant Flag Curvature Spaces and Akbar-Zadeh's Theorem CHAPTER 13 Riemannian Manifolds and Two of Hopf's Theorems CHAPTER 14 Minkowski Spaces, the Theorems of Deicke and Brickell Bibliography Index