The geometry of hyperbolic and elliptic CR-manifolds of codimension two

Abstract

The general theory of parabolic geometries is applied to the study of the normal Cartan connections for all hyperbolic and elliptic 6-dimensional CR-manifolds of codimension two. These structures present a very distinguished case in CR-geometry with many features of the nondegenerate real hypersurfaces. The geometric meaning of the individual components of the torsion is explained and the chains of dimensions one and two are discussed.