  We obtain very sharp results about the lack of validity of the Poincare lemma
for the tangential Cauchy Riemann equations, acting on tangential forms,
tangential to a CR manifold M of general CR dimension n, and general CR
codimension k. This generalizes the classical nonsolvability example of H.
Lewy. We also discuss the CR structure on the characteristic bundle to M, due
to certain degeneracies in the Levi form. A number of naturally geometrically
occuring examples are given.
