Reflection groups on Riemannian manifolds

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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 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.
30 pages, LaTeX, graphicx, psfrag

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Differential Geometry, Group Theory, 51F15, 53C20, 20F55, 22E40}

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http://salesiana.dossiersoluciones.com/handle/123456789/132982

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0306078
 http://arxiv.org/abs/math/0306078
 Annali di Matematica 186 (2006), 25-58

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arXiv