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Cohomogeneity one actions on noncompact symmetric spaces of rank one

Authors:	Jü rgen Berndt Hiroshi Tamaru

Institution:	Department of Mathematics, University College, Cork, Ireland ; Department of Mathematics, Hiroshima University, 1-3-1 Kagamiyama, Higashi- Hiroshima, 739-8526, Japan

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 $\mathbb{C} H^n$ , $n \geq 3$ . For the quaternionic hyperbolic spaces $\mathbb{H} H^n$ , $n \geq 3$ , 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 Élie Cartan.

Keywords:	Symmetric spaces hyperbolic spaces cohomogeneity one actions homogeneous hypersurfaces

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