Cohomogeneity one actions on symmetric spaces of noncompact type

Details Cohomogeneity one actions on symmetric spaces of noncompact type Cohomogeneity one actions on symmetric spaces of noncompact type

2010-06-10

arxiv.org/abs/1006.1980v1

Mathematics

Differential Geometry

28 pages

Scientific paper

An isometric action of a Lie group on a Riemannian manifold is of cohomogeneity one if the corresponding orbit space is one-dimensional. In this article we develop a conceptual approach to the classification of cohomogeneity one actions on Riemannian symmetric spaces of noncompact type in terms of orbit equivalence. As a consequence, we find many new examples of cohomogeneity one actions on Riemannian symmetric spaces of noncompact type. We apply our conceptual approach to derive explicit classifications of cohomogeneity one actions on some symmetric spaces.

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