Cohomogeneity one actions on noncompact symmetric spaces of rank one
Differential Geometry
2007-05-23 v1
Abstract
We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces of dimension greater than two. For the quaternionic hyperbolic spaces of dimension greater than two we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classification problem was essentially solved by Elie Cartan.
Keywords
Cite
@article{arxiv.math/0505490,
title = {Cohomogeneity one actions on noncompact symmetric spaces of rank one},
author = {Jurgen Berndt and Hiroshi Tamaru},
journal= {arXiv preprint arXiv:math/0505490},
year = {2007}
}
Comments
13 pages