Differential geometry
Stability of holomorphically parallelizable manifolds
[Stabilité des variétés holomorphiquement parallélisables]
Comptes Rendus. Mathématique, Tome 353 (2015) no. 8, pp. 741-745.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.06.005
Angella, Daniele 1 ; Tomassini, Adriano 2

1 Istituto Nazionale di Alta Matematica, Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy
2 Dipartimento di Matematica e Informatica, Università di Parma, Parco Area delle Scienze 53/A, 43124 Parma, Italy
@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://www.numdam.org/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://www.numdam.org/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://www.numdam.org/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://www.numdam.org/articles/10.1016/j.crma.2015.06.005/

[1] Andreotti, A.; Stoll, W. Extension of holomorphic maps, Ann. of Math. (2), Volume 72 (1960) no. 2, pp. 312-349

[2] Angella, D. The cohomologies of the Iwasawa manifold and of its small deformations, J. Geom. Anal., Volume 23 (2013) no. 3, pp. 1355-1378

[3] Angella, D.; Kasuya, H. Cohomologies of deformations of solvmanifolds and closedness of some properties, Math. Universalis (2015) (in press) | arXiv

[4] Angella, D.; Kasuya, H. Bott–Chern cohomology of solvmanifolds | arXiv

[5] Angella, D.; Tomassini, A. On the ¯-lemma and Bott–Chern cohomology, Invent. Math., Volume 192 (2013) no. 1, pp. 71-81

[6] Benson, Ch.; Gordon, C.S. Kähler and symplectic structures on nilmanifolds, Topology, Volume 27 (1988) no. 4, pp. 513-518

[7] Bochner, S.; Martin, W.T. Several Complex Variables, Princeton Mathematical Series, vol. 10, Princeton University Press, Princeton, N.J., 1948

[8] Deligne, P.; Griffiths, P.; Morgan, J.; Sullivan, D.P. Real homotopy theory of Kähler manifolds, Invent. Math., Volume 29 (1975) no. 3, pp. 245-274

[9] Demailly, J.-P.; Păun, M. Numerical characterization of the Kähler cone of a compact Kähler manifold, Ann. of Math. (2), Volume 159 (2004) no. 3, pp. 1247-1274

[10] Guan, D. On classification of compact complex solvmanifolds, J. Algebra, Volume 347 (2011) no. 1, pp. 69-82

[11] Hasegawa, K. Minimal models of nilmanifolds, Proc. Amer. Math. Soc., Volume 106 (1989) no. 1, pp. 65-71

[12] Hironaka, H. 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] Kodaira, K.; Spencer, D.C. 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] Nakamura, I. Complex parallelisable manifolds and their small deformations, J. Differ. Geom., Volume 10 (1975) no. 1, pp. 85-112

[15] Narasimhan, R. Several Complex Variables, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1995 (reprint of the 1971 original)

[16] Popovici, D. Deformation limits of projective manifolds: Hodge numbers and strongly Gauduchon metrics, Invent. Math., Volume 194 (2013) no. 3, pp. 515-534

[17] Rollenske, S. The Kuranishi space of complex parallelisable nilmanifolds, J. Eur. Math. Soc., Volume 13 (2011) no. 3, pp. 513-531

[18] Sakane, Y. On compact complex parallelisable solvmanifolds, Osaka J. Math., Volume 13 (1976) no. 1, pp. 187-212

[19] Wang, H.-C. Complex parallisable manifolds, Proc. Amer. Math. Soc., Volume 5 (1954), pp. 771-776

Cité par Sources :