双曲几何讲义-(影印版) 内容简介

one of the main themes of this book is the conflict betweenthe "flexibility' and the "rigidityproperties of the hyperbolicmanifolds： the first radical difference arises between the case ofdimension 2 and the case of higher dimensions （as proved inchapters b and c）， an elementary feature of thus phenomenon beingthe difference between the riemann mapping theorem and liouville'stheorem， as pointed out in chapter a. thus chapter is ratherclementary and most of its material may' be the object of anundergraduate course.together with the rigidity theorem， a basic tool for the study ofhyperbolic manifolds is margulis' lemma， a detailed proof of whichwe give in chapter d; as a consequence of this result in the samechapter we also give a rather accurate description， in alldimensions， of the thin-thick decomposition of a hyperbolicmanifold （especially in case of finite volume）.

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双曲几何讲义-(影印版) 目录

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-spacemodels
a.5 geodesics, hyperbolic subspaces and misceuaneo,s facts
a.6 curvature of hyperbolic space
chapter b.hyperbolic manifolds and the compact two-dimensionalcase
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

双曲几何讲义-(影印版) 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。

双曲几何讲义-(影印版) 目录

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-spacemodels
a.5 geodesics, hyperbolic subspaces and misceuaneo,s facts
a.6 curvature of hyperbolic space
chapter b.hyperbolic manifolds and the compact two-dimensionalcase
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