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Hyperbolic Space

  • Riccardo Benedetti
  • Carlo Petronio
Part of the Universitext book series (UTX)

Abstract

This chapter is devoted to the definition of a Riemannian n-manifold ℍ n called hyperbolic n-space and to the determination of its geometric properties (isometries, geodesies, curvature, etc.). This space is the local model for the class of manifolds we shall deal with in the whole book. The results we are going to prove may be found in several texts (e.g. [Bea], [Co], [Ep2], [Fe], [Fo], [Greenb2], [Mag], [Mask2], [Th1, ch. 3] and [Wol]) so we shall omit precise references. The line of the present chapter is partially inspired by [Ep2], though we shall be dealing with a less general situation. For a wide list of references about hyperbolic geometry from ancient times to 1980 we address the reader to [Mi3].

Keywords

Riemannian Manifold Sectional Curvature Hyperbolic Space Disc Model Conformal Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Riccardo Benedetti
    • 1
  • Carlo Petronio
    • 1
  1. 1.Dipartimento di MatematicaUniversità degli Studi di PisaPisaItaly

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