- 微分几何基础(第2版)(英文版)
- - 作者：(英)普雷斯利
  - 出版社：世界图书出版公司
  - ISBN：9787519200183
  - 出版日期：2016/01/01
  - 页数：473
- 售价：30

内容大纲
微分几何基础讲述的是曲线和平面的微分几何学的主要结论适合于本科生第一个学期的课程。普雷斯利所著的《微分几何基础（第2版）（英文版）》，在改版中有如下新的特征：有一章专门讲述非欧几何，该课题在数学史上具有重要的影响且对现代数学发展的影响也至关重要；书中包括的课题有：平行移动及其应用、地图设色、完整的高斯曲率。
作者介绍
目录
Preface
Contents
1.Curves in the plane and in space
  1.1  What is a curve？
  1.2  Arc-length
  1.3  Reparametrization
  1.4  Closed curves
  1.5  Level curves versus parametrized curves
2.How much does a curve curve？
  2.1  Curvature
  2.2  Plane curves
  2.3  Space curves
3.Global properties of curves
  3.1  Simple closed curves
  3.2  The isoperimetric inequality
  3.3  The four vertex theorem
4.Surfaces in three dimensions
  4.1  What is a surface？
  4.2  Smooth surfaces
  4.3  Smooth maps
  4.4  Tangents and derivatives
  4.5  Normals and orientability
5.Examples of surfaces
  5.1  Level surfaces
  5.2  Quadric surfaces
  5.3  Ruled surfaces and surfaces of revolution
  5.4  Compact surfaces
  5.5  Triply orthogonal systems
  5.6  Applications of the inverse function theorem
6.The flrst fundamental form
  6.1  Lengths of curves on surfaces
  6.2  Isometries of surfaces
  6.3  Conformal mappings of surfaces
  6.4  Equiareal maps and a theorem of Archimedes
  6.5  Sphericalgeometry
7.Curvature of 8urfaces
  7.1  The second fundamental form
  7.2  The Gauss and Weingarten maps
  7.3  Normal and geodesic curvatures
  7.4  Parallel transport and covariant derivative
8.Gaussian， mean and principal curvatures
  8.1  Gaussian and mean curvatures
  8.2  Principal curvatures of a surface
  8.3  Surfaces of constant Gaussian curvature
  8.4  Flat surfaces
  8.5  Surfaces of constant mean curvature
  8.6  Gaussian curvature of compact surfaces
9.Geodesics
  9.1  Definition and basic properties
  9.2  Geodesic equations

  9.3  Geodesics on surfaces of revolution
  9.4  Geodesics as shortest paths
  9.5  Geodesic coordinates
10.Gauss' Theorema Egregium
  10.1  The Gauss and Codazzi-Mainardi equations
  10.2  Gauss' remarkable theorem
  10.3  Surfaces of constant Gaussian curvature
  10.4  Geodesic mappings
11.Hyperbolic geometry
  11.1  Upper half-plane model
  11.2  Isometries of H
  11.3  Poincare disc model
  11.4  Hyperbolic parallels
  11.5  Beltrami-Klein model
12.Minmal surfaces
  12.1  Plateau's problem
  12.2  Examples of minimal surfaces
  12.3  Gauss map of a minimal surface
  12.4  Conformal parametrization of minimal surfaces
  12.5  Minimal surfaces and holomorphic functions
13.The Gauss-Bonnet theorem
  13.1  Gauss-Bonnet for simple closed curves
  13.2  Gauss-Bonnet for curvilinear polygons
  13.3  Integration on compact surfaces
  13.4  Gauss-Bonnet for compact surfaces
  13.5  Map colouring
  13.6  Holonomy and Gaussian curvature
  13.7  Singularities of vector fields
  13.8  Critical points
A0.Inner product spaces and self-adjoint linear maps
A1.Isometries of Euclidean spaces
A2.Mobius transformations
Hints to selected exercises
Solutions
Index

内容大纲

作者介绍

目录

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