Geodesic
The Poincaré lemma and local embeddability
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 2, pp. 393-398

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

For pseudocomplex abstract $CR$ manifolds, the validity of the Poincaré Lemma for $(0,1)$ forms implies local embeddability in $\mathbb{C}^{N}$. The two properties are equivalent for hypersurfaces of real dimension $\geq 5$. As a corollary we obtain a criterion for the non validity of the Poicaré Lemma for $(0,1)$ forms for a large class of abstract $CR$ manifolds of $CR$ codimension larger than one. 
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     title = {The {Poincar\'e} lemma and local embeddability},
     journal = {Bollettino della Unione matematica italiana},
     pages = {393--398},
     publisher = {mathdoc},
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     number = {2},
     year = {2003},
     zbl = {1150.32010},
     mrnumber = {MR1988212},
     language = {en},
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Brinkschulte, Judith; Hill, C. Denson; Nacinovich, Mauro. The Poincaré lemma and local embeddability. Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 2, pp. 393-398. http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_2_a7/