no. 7-8
Geometry
On almost complex structures which are not compatible with symplectic forms
[Sur les structures presque complexes qui ne sont pas compatibles avec des formes symplectiques]

Présenté par : Jean-Pierre Demailly

Vezzoni, Luigi1
1 Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
Comptes Rendus. Mathématique, Tome 349 (2011) no. 7-8, pp. 429-431.

Dans cette Note on démontre que la structure presque complexe sous-jacente à une structure presque hermitienne non kälérienne admettant une connexion compatible avec une torsion antisymétrique ne peut pas, même localement, être calibrée par une forme symplectique.

In this Note we prove that the underlying almost complex structure to a non-Kähler almost Hermitian structure admitting a compatible connection with skew-symmetric torsion cannot be calibrated by a symplectic form even locally.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.01.002
Vezzoni, Luigi 1

1 Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy 
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Vezzoni, Luigi. On almost complex structures which are not compatible with symplectic forms. Comptes Rendus. Mathématique, Tome 349 (2011) no. 7-8, pp. 429-431. doi : 10.1016/j.crma.2011.01.002. http://www.numdam.org/articles/10.1016/j.crma.2011.01.002/

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☆ This work was supported by the Project M.I.U.R. “Riemannian Metrics and Differentiable Manifolds” and by G.N.S.A.G.A. of I.N.d.A.M.