Lectures on hyperbolic geometry

by Benedetti, R.

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Title Statements

Full title :Lectures on hyperbolic geometry / Riccardo Benedetti, Carlo Petronio.

Edition Statements

Publication Date:©1992.

Publication Statements

Publisher(s):Springer-Verlag
Place of Publication:Berlin
Language:eng
Publication Date:©1992.

The Physical Object

Description:xiv, 330 pages : : illustrations ; : 24 cm.

Edition Identifiers

ISBN:354055534X, 9783540555346, 038755534X, 9780387555348
oclc:ocm26012612
LC Classification:QA685
Dewey Decimal:516.9

Ch. 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 Miscellaneous Facts. A.6. Curvature of Hyperbolic Space -- Ch. 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. Teichmuller Space -- Ch. C. The Rigidity Theorem (Compact Case). C.1. First Step of the Proof: Extension of Pseudo-isometries. C.2. Second Step of the Proof: Volume of Ideal Simplices. C.3. Gromov Norm of a Compact Manifold. C.4. Third Step of the Proof: the Gromov Norm and the Volume Are Proportional. C.5. Conclusion of the Proof, Corollaries and Generalizations -- Ch. D. Margulis' Lemma and its Applications. D.1. Margulis' Lemma. D.2. Local Geometry of a Hyperbolic Manifold.

D.3. Ends of a Hyperbolic Manifold -- Ch. E. The Space of Hyperbolic Manifolds and the Volume Function. E.1. The Chabauty and the Geometric Topology. E.2. Convergence in the Geometric Topology: Opening Cus…