The Poincaré lemma and local embeddability
Brinkschulte, Judith ; Hill, C. Denson ; Nacinovich, Mauro
Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003), p. 393-398 / Harvested from Biblioteca Digitale Italiana di Matematica
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For pseudocomplex abstract C⁢R 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 C⁢R manifolds of C⁢R codimension larger than one.

Per varietà C⁢R 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 C⁢R astratte di codimensione C⁢R maggiore di uno.

Publié le : 2003-06-01
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     author = {Judith Brinkschulte and C. Denson Hill and Mauro Nacinovich},
     title = {The Poincar\'e lemma and local embeddability},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {6-A},
     year = {2003},
     pages = {393-398},
     zbl = {1150.32010},
     mrnumber = {1988212},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2003_8_6B_2_393_0}
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Brinkschulte, Judith; Hill, C. Denson; Nacinovich, Mauro. The Poincaré lemma and local embeddability. Bollettino dell'Unione Matematica Italiana, Tome 6-A (2003) pp. 393-398. http://gdmltest.u-ga.fr/item/BUMI_2003_8_6B_2_393_0/

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