Canonical Cartan connection and holomorphic invariants on Engel CR manifolds

Abstract

We describe a complete system of invariants for 4-dimensional CR manifolds of CR dimension 1 and codimension 2 with Engel CR distribution by constructing an explicit canonical Cartan connection. The four essential invariants arising from the Cartan curvature are geometrically interpreted. We also investigate the relationship between the Cartan connection and the normal form of the defining equation of an embedded Engel CR manifold.