曲面几何学
￥ 29.53 ￥ 28 九五品
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浙江杭州
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作者史迪威(John Stillwell)
出版社世界图书出版公司
ISBN9787510005312
出版时间2010-01
版次1
装帧平装
开本16开
纸张胶版纸
页数216页
定价28元
上书时间2024-07-31
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基本信息
书名:曲面几何学
定价：28.00元
作者:史迪威(John Stillwell)
出版社：世界图书出版公司
出版日期：2010-01-01
ISBN：9787510005312
字数：
页码：216
版次：1
装帧：平装
开本：24开
商品重量：
编辑推荐
《曲面几何学》为数学经典教材（）
内容提要
《曲面几何学》揭示了几何和拓扑之间的相互关系，为广大读者介绍了现代几何的基本概况。书的开始介绍了三种简单的面，欧几里得面、球面和双曲平面。运用等距同构群的有效机理，并且将这些原理延伸到常曲率的所有可以用合适的同构方法获得的曲面。紧接着主要是从拓扑和群论的观点出发，讲述一些欧几里得曲面和球面的分类，较为详细地讨论了一些有双曲曲面。由于常曲率曲面理论和现代数学有很大的联系，该书是一本理想的学习几何的入门教程，用简单易行的方法介绍了曲率、群作用和覆盖面。这些理论融合了许多经典的概念，如，复分析、微分几何、拓扑、组合群论和比较热门的分形几何和弦理论。《曲面几何学》内容自成体系，在预备知识部分包括一些线性代数、微积分、基本群论和基本拓扑。
目录
PrefaceChapter 1.The Euclidean Plane1.1 Approaches to Euclidean Geometry1.2 Isometries1.3 Rotations and Reflections1.4 The Three Reflections Theorem1.5 Orientation-Reversing Isometries1.6 Distinctive Features of Euclidean Geometry1.7 DiscussionChapter 2.Euclidean Surfaces2.1 Euclid on Manifolds2.2 The Cylinder2.3 The Twisted Cylinder2.4 The Torus and the Klein Bottle2.5 Quotient Surfaces2.6 A Nondiscontinuous Group2.7 Euclidean Surfaces2.8 Covering a Surface by the Plane2.9 The Covering Isometry Group2.10 DiscussionChapter 3.The Sphere3.1 The Sphere S2 in R33.2 Rotations3.3 Stereographic Projection3.4 Inversion and the Complex Coordinate on the Sphere3.5 Reflections and Rotations as Complex Functions3.6 The Antipodal Map and the Elliptic Plane3.7 Remarks on Groups, Spheres and Projective Spaces3.8 The Area of a Triangle3.9 The Regular Polyhedra3.10 DiscussionChapter 4.The Hyperbolic Plane4.1 Curvature and the Half-Plane4.2 The Half-Plane Model and the Conformal Disc Model4.3 The Three Reflections Theorem4.4 Isometries as Complex Fnctions4.5 Geometric Description of Isometries4.6 Classification of Isometries4.7 The Area of a Triangle4.8 The Projective Disc Model4.9 Hyperbolic Space4.10 DiscussionChapter 5.Hyperbolic Surfaces5.1 Hyperbolic Surfaces and the Killing-Hopf Theorem5.2 The Pseudosphere5.3 The Punctured Sphere5.4 Dense Lines on the Punctured Sphere5.5 General Construction of Hyperbolic Surfaces from Polygons5.6 Geometric Realization of Compact Surfaces5.7 Completeness of Compact Geometric Surfaces5.8 Compact Hyperbolic Surfaces5.9 DiscussionChapter 6.Paths and Geodesics6.1 Topological Classification of Surfaces6.2 Geometric Classification of Surfaces6.3 Paths and Homotopy6.4 Lifting Paths and Lifting Homotopies6.5 The Fundamental Group6.6 Generators and Relations for the Fundamental Group6.7 Fundamental Group and Genus6.8 Closed Geodesic Paths6.9 Classification of Closed Geodesic Paths6.10 DiscussionChapter 7.Planar and Spherical TesseUations7.1 Symmetric Tessellations7.2 Conditions for a Polygon to Be a Fundamental Region7.3 The Triangle Tessellations7.4 Poincarr's Theorem for Compact Polygons7.5 DiscussionChapter 8.Tessellations of Compact Surfaces8.1 Orbifolds and Desingularizations8.2 From Desingularization to Symmetric Tessellation8.3 Desingularizations as (Branched) Coverings8.4 Some Methods of Desingularization8.5 Reduction to a Permutation Problem8.6 Solution of the Permutation Problem8.7 DiscussionReferencesIndex
作者介绍
作者：（澳大利亚）史迪威（John Stillwell）
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