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].
KeywordsRiemannian Manifold Sectional Curvature Hyperbolic Space Disc Model Conformal Geometry
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