Nous montrons un théorème de stabilité pour les familles de variétés holomorphiquement parallélisables, dans la catégorie des variétés hermitiennes.
We prove a stability theorem for families of holomorphically parallelizable manifolds in the category of Hermitian manifolds.
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Daniele Angella 1 ; Adriano Tomassini 2
@article{CRMATH_2015__353_8_741_0, author = {Daniele Angella and Adriano Tomassini}, title = {Stability of holomorphically parallelizable manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {741--745}, publisher = {Elsevier}, volume = {353}, number = {8}, year = {2015}, doi = {10.1016/j.crma.2015.06.005}, language = {en}, }
Daniele Angella; Adriano Tomassini. Stability of holomorphically parallelizable manifolds. Comptes Rendus. Mathématique, Volume 353 (2015) no. 8, pp. 741-745. doi : 10.1016/j.crma.2015.06.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.06.005/
[1] Extension of holomorphic maps, Ann. of Math. (2), Volume 72 (1960) no. 2, pp. 312-349
[2] The cohomologies of the Iwasawa manifold and of its small deformations, J. Geom. Anal., Volume 23 (2013) no. 3, pp. 1355-1378
[3] Cohomologies of deformations of solvmanifolds and closedness of some properties, Math. Universalis (2015) (in press) | arXiv
[4] Bott–Chern cohomology of solvmanifolds | arXiv
[5] On the -lemma and Bott–Chern cohomology, Invent. Math., Volume 192 (2013) no. 1, pp. 71-81
[6] Kähler and symplectic structures on nilmanifolds, Topology, Volume 27 (1988) no. 4, pp. 513-518
[7] Several Complex Variables, Princeton Mathematical Series, vol. 10, Princeton University Press, Princeton, N.J., 1948
[8] Real homotopy theory of Kähler manifolds, Invent. Math., Volume 29 (1975) no. 3, pp. 245-274
[9] Numerical characterization of the Kähler cone of a compact Kähler manifold, Ann. of Math. (2), Volume 159 (2004) no. 3, pp. 1247-1274
[10] On classification of compact complex solvmanifolds, J. Algebra, Volume 347 (2011) no. 1, pp. 69-82
[11] Minimal models of nilmanifolds, Proc. Amer. Math. Soc., Volume 106 (1989) no. 1, pp. 65-71
[12] An example of a non-Kählerian complex-analytic deformation of Kählerian complex structures, Ann. of Math. (2), Volume 75 (1962) no. 1, pp. 190-208
[13] On deformations of complex analytic structures. III. Stability theorems for complex structures, Ann. of Math. (2), Volume 71 (1960) no. 1, pp. 43-76
[14] Complex parallelisable manifolds and their small deformations, J. Differ. Geom., Volume 10 (1975) no. 1, pp. 85-112
[15] Several Complex Variables, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1995 (reprint of the 1971 original)
[16] Deformation limits of projective manifolds: Hodge numbers and strongly Gauduchon metrics, Invent. Math., Volume 194 (2013) no. 3, pp. 515-534
[17] The Kuranishi space of complex parallelisable nilmanifolds, J. Eur. Math. Soc., Volume 13 (2011) no. 3, pp. 513-531
[18] On compact complex parallelisable solvmanifolds, Osaka J. Math., Volume 13 (1976) no. 1, pp. 187-212
[19] Complex parallisable manifolds, Proc. Amer. Math. Soc., Volume 5 (1954), pp. 771-776
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