Download E-books Group Acting on Hyperbolic Space. : Harmonic Analysis and Number Theory PDF

By Fritz Grunewald, Jens Mennicke

This publication is anxious with discontinuous teams of motions of the original attached and easily hooked up Riemannian 3-manifold of continuing curva­ ture -1, that's commonly known as hyperbolic 3-space. This area is the third-dimensional example of an identical Riemannian manifold which exists uniquely in each size n :::: 2. The hyperbolic areas seemed first within the paintings of Lobachevski within the first half the nineteenth century. Very early within the final century the gang of isometries of those areas used to be studied via Steiner, while he checked out the crowd generated via the inversions in spheres. The ge­ ometries underlying the hyperbolic areas have been of primary significance in view that Lobachevski, Bolyai and Gauß had saw that they don't fulfill the axiom of parallels. Already within the classical works a number of concrete coordinate types of hy­ perbolic 3-space have seemed. They make specific computations attainable and likewise supply identifications of the complete crew of motions or isometries with famous matrix teams. One such version, because of H. Poincare, is the higher three half-space IH in JR . the crowd of isometries is then pointed out with an exten­ sion of index 2 of the gang PSL(2,

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