Vitushkin's Germ Theorem for Engel-Type CR Manifolds

Abstract

We study real analytic CR manifolds of CR dimension 1 and codimension 2 in the three-dimensional complex space. We prove that the germ of a holomorphic mapping between 'nonspherical' manifolds can be extended along any path (this is an analog of Vitushkin's germ theorem). For a cubic model surface ('sphere'), we prove an analog of the Poincaré theorem on the mappings of spheres into ℂ². We construct an example of a compact 'spherical' submanifold in a compact complex 3-space such that the germ of a mapping of the 'sphere' into this submanifold cannot be extended to a certain point of the 'sphere'.