Abstract
In this chapter, we study the group of transformations of En generated by reflections in hyperplanes and inversions in spheres. It turns out that this group is isomorphic to the group of isometries of Hn+1. This leads to a deeper understanding of hyperbolic geometry. In Sections 4.5 and 4.6, the conformal 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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© 2006 Springer Science+Business Media, LLC
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(2006). Inversive Geometry. In: Foundations of Hyperbolic Manifolds. Graduate Texts in Mathematics, vol 149. Springer, New York, NY. https://doi.org/10.1007/978-0-387-47322-2_4
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DOI: https://doi.org/10.1007/978-0-387-47322-2_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-33197-3
Online ISBN: 978-0-387-47322-2
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