On cohomogeneity one linear actions on pseudo-Euclidean space [formula omitted

Abstract

The aim of this paper is to study cohomogeneity one isometric linear actions on the p+q-dimensional pseudo-Euclidean space Rp,q. It is proved that the natural isometric action of the nilpotent factor of an Iwasawa decomposition of SO(p,q) is not of cohomogeneity one. The orbits of cohomogeneity one actions of some subgroups of a maximal parabolic subgroup of the isometry group of Rp,q are determined and it is proved that there exist cohomogeneity one isometric actions on Rp,q which are orbit-equivalent on the complement of a p-dimensional degenerate subspace Wp of Rp,q and not orbit-equivalent on Wp.