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双曲几何讲义-(影印版)

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作者：本尼迪特

出版社：世界图书出版公司

本类榜单：自然科学

分类：自然科学 > 数学 > 几何与拓扑

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woo***（二星用户）

双曲几何介绍

对双曲几何的介绍深入浅出，值得一读。

2015-01-07 00:46:01

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图文详情

ISBN：9787510046322
装帧：一般胶版纸
册数：暂无
重量：暂无
开本：24开
页数：330
出版时间：2012-08-01
条形码：9787510046322 ; 978-7-5100-4632-2

本书特色

Riccardo Benedetti、Carlo Petronio所著的《双曲几何讲义》是一部讲述双曲几何的本科生教程，重点强调双曲流形上的几何。旨在为读者全面讲述基础结果，独立性强，完整，详尽，自成体系。在讲述双曲空间的经典材料和Teichmüller空间之后，接着以Mostow 刚性定理和Margulis定理这两个基本结论为核心展开讲述。这些形成了学习Chabauty和几何拓扑的基础；并且深入全面地剖析了Wang定理和 Jorgensen-Thurston 理论，给予讲述三维例子很大的空间；同时，以依附于理想四面体的三流形表示为基础，全面介绍了双曲手术定理。

内容简介

　　one of the main themes of this book is the conflict between the "flexibility' and the "rigidity　properties of the hyperbolic manifolds： the first radical difference arises between the case of dimension 2 and the case of higher dimensions （as proved in chapters b and c）， an elementary feature of thus phenomenon being the difference between the riemann mapping theorem and liouville's theorem， as pointed out in chapter a. thus chapter is rather clementary and most of its material may' be the object of an undergraduate course. 　　together with the rigidity theorem， a basic tool for the study of hyperbolic manifolds is margulis' lemma， a detailed proof of which we give in chapter d; as a consequence of this result in the same chapter we also give a rather accurate description， in all dimensions， of the thin-thick decomposition of a hyperbolic manifold （especially in case of finite volume）.

preface
chapter a.hyperbolic space
　a.1 models for hyperbolic space
　a.2 isometries of hyperbolic space: hyperboloid model
　a.3 conformal geometry
　a.4 isometries of hyperbolic space: disc and half-space models
　a.5 geodesics, hyperbolic subspaces and misceuaneo,s facts
　a.6 curvature of hyperbolic space
chapter b.hyperbolic manifolds and the compact two-dimensional case
　b.1 hyperbolic, elliptic and flat manifolds
　b.2 topology of compact oriented surfaces
　b.3 hyperbolic, elliptic and flat surfaces
　b.4 teichmiiller space
chapter c.the rigidity theorem (compact case)
　c.1 first step of the proof: extension of pseudo-isometrics

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