Let be a relatively closed subset of a Stein manifold. We prove that the -cohomology groups of Whitney forms on and of currents supported on are either zero or infinite dimensional. This yields obstructions of the existence of a generic embedding of a CR manifold into any open subset of any Stein manifold, namely by the nonvanishing but finite dimensionality of some intermediate -cohomology groups.
Convergence of special Green integrals for matrix factorization of the Laplace operator in is proved. Explicit formulae for solutions of -equation in strictly pseudo-convex domains in are obtained.
There is a well known one–parameter family of left invariant CR structures on . We show how purely algebraic methods can be used to explicitly compute the canonical Cartan connections associated to these structures and their curvatures. We also obtain explicit descriptions of tractor bundles and tractor connections.
In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As an application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms of its holonomy representation.