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    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
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Groups Acting on Hyperbolic Space: Harmonic Analysis and Number Theory

Groups Acting on Hyperbolic Space: Harmonic Analysis and Number Theory

Elstrodt, Juergen
Grunewald, Fritz
Mennicke, Jens

Hardcover

Series: Springer Monographs in Mathematics

AlgebraGeneral Mathematics

ISBN10: 3540627456
ISBN13: 9783540627456
Publisher: Springer Nature
Published: Nov 12 1997
Pages: 524
Weight: 1.94
Height: 1.36 Width: 6.52 Depth: 9.44
Language: English
This book is concerned with discontinuous groups of motions of the unique connected and simply connected Riemannian 3-manifold of constant curva- ture -1, which is traditionally called hyperbolic 3-space. This space is the 3-dimensional instance of an analogous Riemannian manifold which exists uniquely in every dimension n:::: 2. The hyperbolic spaces appeared first in the work of Lobachevski in the first half of the 19th century. Very early in the last century the group of isometries of these spaces was studied by Steiner, when he looked at the group generated by the inversions in spheres. The ge- ometries underlying the hyperbolic spaces were of fundamental importance since Lobachevski, Bolyai and Gau had observed that they do not satisfy the axiom of parallels. Already in the classical works several concrete coordinate models of hy- perbolic 3-space have appeared. They make explicit computations possible and also give identifications of the full group of motions or isometries withwell-known matrix groups. One such model, due to H. Poincare, is the upper 3 half-space IH in JR . The group of isometries is then identified with an exten- sion of index 2 of the group PSL(2,

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