Strictly nearly Kähler 6-manifolds are not compatible with symplectic forms

Mehdi Lejmi

doi:10.1016/j.crma.2006.10.017

Differential Geometry

Strictly nearly Kähler 6-manifolds are not compatible with symplectic forms
[Les variétés strictement approximativement kählérienne de dimension 6 et les formes symplectiques]

Présenté par : Étienne Ghys

Mehdi Lejmi ¹

¹ Département de Mathématiques, UQAM, C.P. 8888, Succ. Centre-ville, Montréal (Québec), H3C 3P8, Canada

Comptes Rendus. Mathématique, Volume 343 (2006) no. 11-12, pp. 759-762.

Résumé
Abstract

Nous démontrons que la structure presque-complexe d'une variété nearly-kählérienne non-intégrable de dimension 6-en particulier la structure presque-complexe standard sur la sphère $S^{6}$ -ne peut pas être compatible avec une forme symplectque.

We show that the almost complex structure underlying a non-Kähler, nearly Kähler 6-manifold (in particular, the standard almost complex structure of $S^{6}$ ) cannot be compatible with any symplectic form, even locally.

Reçu le : 2006-06-15
Accepté le : 2006-10-15
Publié le : 2006-11-20

DOI : 10.1016/j.crma.2006.10.017

Affiliations des auteurs :

Mehdi Lejmi ¹

¹ Département de Mathématiques, UQAM, C.P. 8888, Succ. Centre-ville, Montréal (Québec), H3C 3P8, Canada

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     title = {Strictly nearly {K\"ahler} 6-manifolds are not compatible with symplectic forms},
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     year = {2006},
     doi = {10.1016/j.crma.2006.10.017},
     language = {en},
}

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Mehdi Lejmi. Strictly nearly Kähler 6-manifolds are not compatible with symplectic forms. Comptes Rendus. Mathématique, Volume 343 (2006) no. 11-12, pp. 759-762. doi : 10.1016/j.crma.2006.10.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.10.017/

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