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

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For pseudocomplex abstract CR manifolds, the validity of the Poincaré Lemma for (0,1) forms implies local embeddability in CN. The two properties are equivalent for hypersurfaces of real dimension ≥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.
Per varietà CR astratte pseudoconvesse la validità del Lemma di Poincaré per forme di tipo (0,1) implica l'immergibilità locale in CN; le due proprietà sono equivalenti per ipersuperfici di dimensione reale ≥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