Cohomogeneity one actions on noncompact symmetric spaces with a totally geodesic singular orbit
An isometric action of a connected Lie group on a Riemannian manifold \(M\) is of cohomogeneity one if the codimension of a generic orbit is one. One problem is to classify such actions on a given manifold. When \(M\) is a Riemannian symmetric space of noncompact type, such an action induces either a foliation or has exactly one singular orbit. The classification in the former case is known by the authors in [J. Differ. Geom 63, 1--40 (2003; Zbl 1070.53011)]. This paper classifies such actions for the second case under the assumption that the singular orbit is a totally geodesic submanifold. This condition is satisfied when the dimension of the singular orbit is small.
scientific article; zbMATH DE number 2114241