Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank

Abstract

We develop a new structural result for cohomogeneity one actions on (not necessarily irreducible) symmetric spaces of noncompact type and arbitrary rank. We apply this result to classify cohomogeneity one actions on the spaces SLn(R)/SOn, n ≥ 2, up to orbit equivalence. We also reduce the classification problem on a reducible space to the classification on each one of its irreducible factors, which in particular allows to classify cohomogeneity one actions on any f inite product of hyperbolic spaces.