Reflection groups on Riemannian manifolds

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 Rie...

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Bibliographic Details
Published inAnnali di matematica pura ed applicata Vol. 186; no. 1
Main Authors Alekseevsky, Dmitri V., Kriegl, Andreas, Losik, Mark, Michor, Peter W.
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.01.2007
Subjects
Intersections
Isotropy
Riemann manifold
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Summary: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.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-005-0166-4