张量与黎曼几何：微分方程应用（英文版）
作者： Nail H.Ibragimov
出版时间：2015-04
出版社：高等教育出版社
- 高等教育出版社
- 9787040423853
- 1版
- 98615
- 48265953-9
- 精装
- 16开
- 2015-04
- 170
- 187
- O186.12
- 数学、统计类
- 本科 研究生及以上
《张量与黎曼几何(微分方程应用英文版)(精)/非线性物理科学》是作者在俄罗斯、法国、 南非和瑞典多年讲授黎曼几何与张量课程讲义的基础 上整理而成。本书通俗易懂、叙述清晰。通过阅读本 书，读者将轻松掌握应用张量、黎曼几何的理论以及 几何化的方法求解偏微分方程，尤其是利用近似重整 化群理论将大大简化de Sitter 空间中广义相对论方 程的求解。
Nail H. Ibragimov教授为瑞典科学家，被公认为是在微分方程对称分析方面世界上最具权威的专家 之一。他发起并构建了现代群分析理论和应用方面很多新的发展。
前辅文
Part I Tensors and Riemannian spaces
1 Preliminaries
1.1 Vectors in linear spaces
1.2 Index notationSummation convention
Exercises
2 Conservation laws
2.1 Conservation laws in classical mechanics
2.2 General discussion of conservation laws
2.3 Conserved vectors defined by symmetries
Exercises
3 Introduction of tensors and Riemannian spaces
3.1 Tensors
3.2 Riemannian spaces
3.3 Application to ODEs
Exercises
4 Motions in Riemannian spaces
4.1 Introduction
4.2 Isometric motions
4.3 Conformal motions
4.4 Generalized motions
Exercises
Part II Riemannian spaces of second-order equations
5 Riemannian spaces associated with linear PDEs
5.1 Covariant form of second-order equations
5.2 Conformally invariant equations
Exercises
6 Geometry of linear hyperbolic equations
6.1 Generalities
6.2 Spaces with nontrivial conformal group
6.3 Standard form of second-order equations
Exercises
7 Solution of the initial value problem
7.1 The Cauchy problem
7.2 Geodesics in spaces with nontrivial conformal group
7.3 The Huygens principle
Exercises
Part III Theory of relativity
8 Brief introduction to relativity
8.1 Special relativity
8.2 The Maxwell equations
8.3 The Dirac equation
8.4 General relativity
Exercises
9 Relativity in de Sitter space
9.1 The de Sitter space
9.2 The de Sitter group
9.3 Approximate de Sitter group.
9.4 Motion of a particle in de Sitter space
9.5 Curved wave operator.
9.6 Neutrinos in de Sitter space
Exercises
Bibliography
Index
