Voir la notice de l'article provenant de la source Numdam
We prove a stability theorem for families of holomorphically parallelizable manifolds in the category of Hermitian manifolds.
Nous montrons un théorème de stabilité pour les familles de variétés holomorphiquement parallélisables, dans la catégorie des variétés hermitiennes.
Angella, Daniele 1 ; Tomassini, Adriano 2
@article{CRMATH_2015__353_8_741_0, author = {Angella, Daniele and Tomassini, Adriano}, 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}, url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2015.06.005/} }
TY - JOUR AU - Angella, Daniele AU - Tomassini, Adriano TI - Stability of holomorphically parallelizable manifolds JO - Comptes Rendus. Mathématique PY - 2015 SP - 741 EP - 745 VL - 353 IS - 8 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2015.06.005/ DO - 10.1016/j.crma.2015.06.005 LA - en ID - CRMATH_2015__353_8_741_0 ER -
%0 Journal Article %A Angella, Daniele %A Tomassini, Adriano %T Stability of holomorphically parallelizable manifolds %J Comptes Rendus. Mathématique %D 2015 %P 741-745 %V 353 %N 8 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2015.06.005/ %R 10.1016/j.crma.2015.06.005 %G en %F CRMATH_2015__353_8_741_0
Angella, Daniele; Tomassini, Adriano. Stability of holomorphically parallelizable manifolds. Comptes Rendus. Mathématique, Tome 353 (2015) no. 8, pp. 741-745. doi : 10.1016/j.crma.2015.06.005. http://geodesic.mathdoc.fr/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
Cité par Sources :