Geometry
On almost complex structures which are not compatible with symplectic forms

Presented by: Jean-Pierre Demailly

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

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.

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.

Received:
Accepted:
Published online:
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, Volume 349 (2011) no. 7-8, pp. 429-431. doi : 10.1016/j.crma.2011.01.002. https://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.