Dans cette note, nous construisons, pour chaque , une variété compacte complexe non Kähler X de dimension complexe n admettant une métrique equilibrée et une métrique asthéno-Kähler ; de plus, cette métrique est k-ième Gauduchon pour .
In this note, we construct, for every , a non-Kähler compact complex manifold X of complex dimension n admitting a balanced metric and an astheno-Kähler metric, which is in addition k-th Gauduchon for any .
Accepté le :
Publié le :
Adela Latorre 1 ; Luis Ugarte 1
@article{CRMATH_2017__355_1_90_0, author = {Adela Latorre and Luis Ugarte}, title = {On {non-K\"ahler} compact complex manifolds with balanced and {astheno-K\"ahler} metrics}, journal = {Comptes Rendus. Math\'ematique}, pages = {90--93}, publisher = {Elsevier}, volume = {355}, number = {1}, year = {2017}, doi = {10.1016/j.crma.2016.11.004}, language = {en}, }
Adela Latorre; Luis Ugarte. On non-Kähler compact complex manifolds with balanced and astheno-Kähler metrics. Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 90-93. doi : 10.1016/j.crma.2016.11.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.11.004/
[1] Vanishing theorems on Hermitian manifolds, Differ. Geom. Appl., Volume 14 (2001), pp. 251-265
[2] Classification of Abelian complex structures on 6-dimensional Lie algebras, J. Lond. Math. Soc. (2), Volume 83 (2011) no. 1, pp. 232-255 (Corrigendum)
[3] Obstructions to the existence of Kähler structures on compact complex manifolds, Proc. Amer. Math. Soc., Volume 142 (2014), pp. 3561-3568
[4] Astheno-Kähler and balanced structures on fibrations | arXiv
[5] On astheno-Kähler metrics, J. Lond. Math. Soc., Volume 83 (2011), pp. 290-308
[6] On generalized Gauduchon metrics, Proc. Edinb. Math. Soc., Volume 56 (2013), pp. 733-753
[7] Special Hermitian metrics on compact solvmanifolds, J. Geom. Phys., Volume 91 (2015), pp. 40-53
[8] On the existence of balanced and SKT metrics on nilmanifolds, Proc. Amer. Math. Soc., Volume 144 (2016), pp. 2455-2459
[9] Semilinear equations, the function, and generalized Gauduchon metrics, J. Eur. Math. Soc., Volume 15 (2013), pp. 659-680
[10] La 1-forme de torsion d'une variété hermitienne compacte, Math. Ann., Volume 267 (1984), pp. 495-518
[11] Vanishing theorems and string backgrounds, Class. Quantum Gravity, Volume 18 (2001), pp. 1089-1110
[12] Vanishing theorems on -strong Kähler manifolds with torsion, Adv. Math., Volume 237 (2013), pp. 147-164
[13] A non-linear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry, Acta Math., Volume 170 (1993), pp. 221-254 (Corrigendum)
[14] On compact astheno-Kähler manifolds, Colloq. Math., Volume 89 (2001), pp. 213-221
[15] On the existence of special metrics in complex geometry, Acta Math., Volume 149 (1982), pp. 261-295
[16] Gauduchon metrics with prescribed volume form | arXiv
Cité par Sources :
Commentaires - Politique