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

Presented by: Étienne Ghys

Mehdi Lejmi ¹

¹Département 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

Abstract (Original language)
Résumé

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.

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.

Received: 2006-06-15
Accepted: 2006-10-15
Published online: 2006-11-20

DOI: 10.1016/j.crma.2006.10.017

Author's affiliations:

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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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

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