Comptes Rendus
no. 11-12
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 Lejmi1
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.

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 S6-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 S6) cannot be compatible with any symplectic form, even locally.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.10.017

Mehdi Lejmi 1

1 Département de Mathématiques, UQAM, C.P. 8888, Succ. Centre-ville, Montréal (Québec), H3C 3P8, Canada 
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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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  • Qiang Tan; Hongyu Wang; Jiuru Zhou; Peng Zhu On Tamed Almost Complex Four-Manifolds, Peking Mathematical Journal, Volume 5 (2022) no. 1, p. 37 | DOI:10.1007/s42543-021-00045-7
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