Homogeneous Levi degenerate CR-manifolds in dimension 5

We investigate CR-manifolds which are tubes M:= F x iV over general bases F in a real vector space V and characterize the k-nondegeneracy of M in terms of the real affine geometry of F. We give a method for an explicit computation of the Lie algebra hol(M,a) of all local infinitesimal CR-transformations at a and use these local invariants to establish the CR-inequivalence of certain families of CR-manifolds. In dimension 5 we present, apart from the well known tube over the future light cone, new examples of 2-nondegenerate homogeneous CR-manifolds that are mutually locally CR-inequivalent.