On the failure of the Poincar\'e Lemma for de-bar-sub-M II
Differential Geometry
2007-10-19 v1 Analysis of PDEs
Complex Variables
Abstract
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.
Keywords
Cite
@article{arxiv.0710.3573,
title = {On the failure of the Poincar\'e Lemma for de-bar-sub-M II},
author = {C. Denson Hill and Mauro Nacinovich},
journal= {arXiv preprint arXiv:0710.3573},
year = {2007}
}