Reflection groups on Riemannian manifolds.

Autor: Dmitri Alekseevsky, Andreas Kriegl, Mark Losik
Zdroj: Annali di Matematica Pura ed Applicata; Jan2007, Vol. 186 Issue 1, p25-58, 34p
Abstrakt: 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. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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