Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank
arXiv:2202.05138 · doi:10.1016/j.aim.2023.109165
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 SL(n,R)/SO(n), n>1, 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 finite product of hyperbolic spaces.
30 pages