No 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. We also investigate the relation between the Cartan connection and the normal form of the defining equation of an embedded Engel CR manifold.

No abstract

No abstract

The model 4-dimensional CR-cubic in C 3 has the following "model" property: it is (essentially) the unique locally homogeneous 4-dimensional CR-manifold in C 3 with finite-dimensional infinitesimal automorphism algebra g and non-trivial isotropy subalgebra. We study and classify, up to local biholomorphic equivalence, all g-homogeneous hypersurfaces in C 3 and also classify the corresponding local transitive actions of the model algebra g on hypersurfaces in C 3 .