On the absence of the one-sided Poincaré lemma in Cauchy-Riemann manifolds
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 4 (2005) no. 4, p. 587-600

Given an embeddable $CR$ manifold $M$ and a non-characteristic hypersurface $S\subset M$ we present a necessary condition for the tangential Cauchy-Riemann operator ${\overline{\partial }}_{M}$ on $M$ to be locally solvable near a point ${x}_{0}\in S$ in one of the sides determined by $S$.

Classification:  32W10,  58J10
@article{ASNSP_2005_5_4_4_587_0,
author = {Nicola, Fabio},
title = {On the absence of the one-sided Poincar\'e lemma in Cauchy-Riemann manifolds},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 4},
number = {4},
year = {2005},
pages = {587-600},
zbl = {1170.32315},
mrnumber = {2207735},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2005_5_4_4_587_0}
}

Nicola, Fabio. On the absence of the one-sided Poincaré lemma in Cauchy-Riemann manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 4 (2005) no. 4, pp. 587-600. http://www.numdam.org/item/ASNSP_2005_5_4_4_587_0/

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