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雙曲幾何講義-(影印版) 版權信息
- ISBN：9787510046322
- 條形碼：9787510046322 ; 978-7-5100-4632-2
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>>
雙曲幾何講義-(影印版) 本書特色
Riccardo Benedetti、Carlo Petronio所著的《雙曲幾何講義》是一部講述雙曲幾何的本科生教程，重點強調雙曲流形上的幾何。旨在為讀者全面講述基礎結果，獨立性強，完整，詳盡，自成體系。在講述雙曲空間的經典材料和Teichmüller空間之后，接著以Mostow 剛性定理和Margulis定理這兩個基本結論為核心展開講述。這些形成了學習Chabauty和幾何拓撲的基礎；并且深入全面地剖析了Wang定理和 Jorgensen-Thurston 理論，給予講述三維例子很大的空間；同時，以依附于理想四面體的三流形表示為基礎，全面介紹了雙曲手術定理。
雙曲幾何講義-(影印版) 內容簡介
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）.
雙曲幾何講義-(影印版) 目錄
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
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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