LAUSR

Abstract The aim of this paper is to study cohomogeneity one isometric linear actions on the p + q -dimensional pseudo-Euclidean space R p , q . It is proved that the natural isometric action of the nilpotent factor of an Iwasawa decomposition of S O ( 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 R p , q are determined and it is proved that there exist cohomogeneity one isometric actions on R p , q which are orbit-equivalent on the complement of a p-dimensional degenerate subspace W p of R p , q and not orbit-equivalent on W p .