Abstract
In this chapter, we study the group of transformations of E n generated by reflections in hyperplanes and inversions in spheres. It turns out that this group is isomorphic to the group of isometries of H n+1. This leads to a deeper understanding of hyperbolic geometry. In Sections 4.5 and 4.6, the conformai ball and upper half-space models of hyperbolic n-space are introduced. The chapter ends with a geometric analysis of the isometries of hyperbolic n-space.
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© 1994 Springer Science+Business Media New York
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Ratcliffe, J.G. (1994). Inversive Geometry. In: Foundations of Hyperbolic Manifolds. Graduate Texts in Mathematics, vol 149. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4013-4_4
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DOI: https://doi.org/10.1007/978-1-4757-4013-4_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94348-0
Online ISBN: 978-1-4757-4013-4
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