Reflection groups on Riemannian manifolds |
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Authors: | Dmitri V. Alekseevsky Andreas Kriegl Mark Losik Peter W. Michor |
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Affiliation: | 1.Department of Mathematics,University of Hull,Hull,England;2.Fakult?t für Mathematik,Universit?t Wien,Wien,Austria;3.Saratov State University,Saratov,Russia;4.Erwin Schr?dinger Institute of Mathematical Physics,Wien,Austria |
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Abstract: | We investigate discrete groups G of isometries of a complete connected Riemannian manifold M which are generated by reflections, in particular those generated by disecting reflections. We show that these are Coxeter groups, and that the orbit space M/G is isometric to a Weyl chamber C which is a Riemannian manifold with corners and certain angle conditions along intersections of faces. We can also reconstruct the manifold and its action from the Riemannian chamber and its equipment of isotropy group data along the faces. We also discuss these results from the point of view of Riemannian orbifolds. Mathematics Subject Classification Primary 51F15, 53C20, 20F55, 22E40 |
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Keywords: | Reflection groups Isometries |
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