On the failure of the Poincaré Lemma for de-bar-sub-M II

Details On the failure of the Poincaré Lemma for de-bar-sub-M II On the failure of the Poincaré Lemma for de-bar-sub-M II

2007-10-18

arxiv.org/abs/0710.3573v1

Math. Ann. 335 (2006), 193-219

Mathematics

Differential Geometry

Scientific paper

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.

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