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 dans Biblioteca Digitale Italiana di Matematica

Per varietà $CR$ astratte pseudoconvesse la validità del Lemma di Poincaré per forme di tipo $(0,1)$ implica l'immergibilità locale in $\mathbb{C}^{N}$; le due proprietà sono equivalenti per ipersuperfici di dimensione reale $\geq 5$. Come corollario si ottiene un criterio per la non validità del Lemma di Poincaré per forme di tipo $(0,1)$ per una vasta classe di varietà $CR$ astratte di codimensione $CR$ maggiore di uno. 
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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. https://geodesic-test.mathdoc.fr/item/BUMI_2003_8_6B_2_a7/

[A] T. Akahori, A new approach to the local embedding theorem of $CR$-structures for $n \geq 4$, Mem. Amer. Math. Soc., 366 (1987), Amer. Math. Soc. Providence R.I. | MR | Zbl

[AFN] A. Andreotti-G. Fredricks-M. Nacinovich, On the absence of Poincaré lemma in tangential Cauchy-Riemann complexes, Ann. Sc. Norm. Sup. Pisa, 8 (1981), 365-404. | fulltext mini-dml | MR | Zbl

[AH] A. Andreotti-C. D. Hill, E.E. Levi convexity and the Hans Lewy problem I, II, Ann. Sc. norm. sup. Pisa, 26 (1972), 325-363, 747-806. | Zbl

[B] L. Boutet De Monvel, Intégration des équations de Cauchy-Riemann induites formelles, Sem. Goulaouic-Lions-Schwartz (1974-1975). | fulltext mini-dml | MR | Zbl

[HN1] C. D. Hill-M. Nacinovich, A weak pseudoconcavity condition for abstract almost $CR$ manifolds, Invent. Math., 142 (2000), 251-283. | MR | Zbl

[HN2] C. D. Hill-M. Nacinovich, On the failure of the Poincaré lemma for the $\bar\partial_{M^-}$ complex, Quaderni sez. Geometria Dip. Matematica Pisa, 1.260.1329 (2001), 1-10.

[Hö] L. Hörmander, Linear Partial Differential Operators, Springer, Berlin (1963). | MR

[JT] H. Jacobowitz-F. Treves, Aberrant $CR$ structures, Hokkaido Math. Jour., 12 (1983), 276-292. | MR | Zbl

[K] M. Kuranishi, Strongly pseudoconvex CR structures over small balls I-III, Ann. of Math., 115, 116 (1982), 451-500, 1-64, 249-330. | MR | Zbl

[N] M. Nacinovich, On the absence of Poincaré lemma for some systems of partial differential equations, Compos. Math., 44 (1981), 241-303. | fulltext mini-dml | MR | Zbl

[Ni] L. Nirenberg, On a problem of Hans Lewy, Uspeki Math. Naut, 292 (1974), 241-251. | MR | Zbl

[R] H. Rossi, LeBrun's nonrealizability theory in higher dimensions, Duke Math. J., 52 (1985), 457-474. | fulltext mini-dml | MR | Zbl

[W] S. Webster, On the proof of Kuranishi's embedding theorem, Ann. Inst. H. Poincaré, 9 (1989), 183-207. | fulltext mini-dml | MR | Zbl