The Poincare lemma and local embeddability

Details The Poincare lemma and local embeddability The Poincare lemma and local embeddability

2007-11-02

arxiv.org/abs/0711.0227v1

Bollettino U.M.I. (8) 6-B (2003), 393-398

Mathematics

Complex Variables

Scientific paper

For pseudoconvex abstract CR manifolds, the validity of the Poincare Lemma
for (0,1) forms implies local embeddability in C^N. The two properties are
equivalent for hypersurfaces of real dimension > or = 5. As a corollary we
obtain a criterion for the non validity of the Poicare Lemma for (0,1) forms
for a large class of abstract CR manifolds of CR codimension larger than one.

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