CR-manifolds of codimension two of parabolic type

Abstract

For CR-manifolds in C 4 with the Levi form at the origin of parabolic type we construct an analogue of the Chern-Moser normal form for Levi non-degenerate hypersurfaces. The group of transformations which map a given CR manifold of parabolic type into a normal form is shown to be isomorphic with the isotropy group of the osculating parabolic quadric at the origin.