Singular Orbits in Cohomogeneity One Pseudo-Euclidean Space Rν4

The purpose of this paper is to study cohomogeneity one pseudo-Euclidean space R-nu(4), 0 <= nu <= 4, under a proper action of a connected Lie subgroupG subset of I so(R-nu(4)). Among other results, when there is a singular orbit B, we determine the representation of the acting group G in SOo (nu, 4 - nu) x 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{nu, 4 - nu}.