- 现代几何学方法和应用(第1卷英文版)
- - 作者：B.A.Dubrovin//A.T.Fomenko//S.P.Novikov|责编:刘慧//高蓉
  - 出版社：世界图书出版公司
  - ISBN：9787506201230
  - 出版日期：1999/11/01
  - 页数：464
- 售价：43.6

内容大纲
本书是以苏联莫斯科大学数力系的几何课讲义为基础形成的。它全面介绍现代几何学的基本概念和定理，并特别强调在数学其他分支以及理论物理中的应用。语言通俗易懂，尽量使物理工作者易于人门。第1卷主要论述曲面几何学、变换群和几何场论等课题，包括张量及其变分计算、一维和多维变分法等内容。
作者介绍
目录
CHAPTER 1 Geometry in Regions of a Space. Basic Concepts
  1. Co-ordinate systems
    1.1. Cartesian co-ordinates in a space
    1.2. Co-ordinate changes
  2. Euclidean space
    2.1. Curves in Euclidean space
    2.2. Quadratic forms and vectors
  3. Riemannian and pseudo-Riemannian spaces
    3.1. Riemannian metrics
    3.2. The Minkowski metric
  4. The simplest groups of transformations of Euclidean space
    4.1. Groups of transformations of a region
    4.2. Transformations of the plane
    4.3. The isometries of 3-dimensional Euclidean space
    4.4. Further examples of transformation groups
    4.5. Exercises
  5. The Serret-Frenet formulae
    5.1. Curvature of curves in the Euclidean plane
    5.2. Curves in Euclidean 3-space. Curvature and torsion
    5.3. Orthogonal transformations depending on a parameter
    5.4. Exercises
  6. Pseudo-Euclidean spaces
    6.1. The simplest concepts of the special theory of relativity
    6.2. Lorentz transformations
    6.3. Exercises
CHAPTER 2 The Theory of Surfaces
  7. Geometry on a surface in space
    7.1. Co-ordinates on a surface
    7.2. Tangent planes
    7.3. The metric on a surface in Euclidean space
    7.4. Surface area
    7.5. Exercises
  8. The second fundamental form
    8.1. Curvature of curves on a surface in Euclidean space
    8.2. Invariants of a pair of quadratic forms
    8.3. Properties of the second fundamental form
    8.4. Exercises
  9. The metric on the sphere
  10. Space-like surfaces in pseudo-Euclidean space
    10.1. The pseudo-sphere
    10.2. Curvature of space-like curves in R3
  11. The language of complex numbers in geometry
    11.1. Complex and real co-ordinates
    11.2. The Hermitian scalar product
    11.3. Examples of complex transformation groups
  12. Analytic functions
    12.1. Complex notation for the element of length, and for the differential of a function
    12.2. Complex co-ordinate changes
    12.3. Surfaces in complex space
  13. The conformal form of the metric on a surface

    13.1. Isothermal co-ordinates. Gaussian curvature in terms of conformal co-ordinates
    13.2. Conformal form of the metrics on the sphere and the Lobachevskian plane
    13.3. Surfaces of constant curvature
    13.4. Exercises
  14. Transformation groups as surfaces in N-dimensional space
    14.1. Co-ordinates in a neighbourhood of the identity
    14.2. The exponential function with matrix argument
    14.3. The quaternions
    14.4. Exercises
  15. Conformal transformations of Euclidean and pseudo-Euclidean spaces of several dimensions
CHAPTER 3 Tensors: The Algebraic Theory
  16. Examples of tensors
  17. The general definition of a tensor
    17.1. The transformation rule for the components of a tensor of arbitrary rank
……
CHAPTER 4 The Differential Calculus of Tensors
CHAPTER 5 The Elements of the Calculus of Variations
CHAPTER 6 The Calculus of Variations in Several Dimensions. Fields and Their Geometric Invariants
Bibliography
Index

内容大纲

作者介绍

目录

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