On the symmetry algebras of 5-dimensional CR-manifolds

Abstract

We show that for a real-analytic connected holomorphically nondegenerate 5-dimensional CR-hypersurface M and its symmetry algebra s one has either: (i) dim⁡s=15 and M is spherical (with Levi form of signature either (2,0) or (1,1) everywhere), or (ii) dim⁡s≤11 where dim⁡s=11 can only occur if on a dense open subset M is spherical with Levi form of signature (1,1). Furthermore, we construct a series of examples of pairwise nonequivalent CR-hypersurfaces with dim⁡s=11.