Abstract

The purpose of this paper is to study cohomogeneity one pseudo Euclidean space R^4_v, under a proper action of a connected Lie subgroup G of  Iso(R^4_v). Among other results, when there is a singular orbit B, we determine the representation of the acting group G in $SO(v,4−v) ltimes R^4$ up to conjugacy, then the orbits up to isometry. In particular, we prove that B is an affine pseudo Euclidean subspace with dimB > min{v,4−v }.