Reflection groups on Riemannian manifolds

Details Reflection groups on Riemannian manifolds Reflection groups on Riemannian manifolds

2003-06-04

arxiv.org/abs/math/0306078v1

Annali di Matematica 186 (2006), 25-58

Mathematics

Differential Geometry

30 pages, LaTeX, graphicx, psfrag

Scientific paper

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.

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