[Les variétés strictement approximativement kählérienne de dimension 6 et les formes symplectiques]
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 -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 ) cannot be compatible with any symplectic form, even locally.
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@article{CRMATH_2006__343_11-12_759_0,
author = {Lejmi, Mehdi},
title = {Strictly nearly {K\"ahler} 6-manifolds are not compatible with symplectic forms},
journal = {Comptes Rendus. Math\'ematique},
pages = {759--762},
publisher = {Elsevier},
volume = {343},
number = {11-12},
year = {2006},
doi = {10.1016/j.crma.2006.10.017},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.10.017/}
}
TY - JOUR AU - Lejmi, Mehdi TI - Strictly nearly Kähler 6-manifolds are not compatible with symplectic forms JO - Comptes Rendus. Mathématique PY - 2006 SP - 759 EP - 762 VL - 343 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.10.017/ DO - 10.1016/j.crma.2006.10.017 LA - en ID - CRMATH_2006__343_11-12_759_0 ER -
%0 Journal Article %A Lejmi, Mehdi %T Strictly nearly Kähler 6-manifolds are not compatible with symplectic forms %J Comptes Rendus. Mathématique %D 2006 %P 759-762 %V 343 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.10.017/ %R 10.1016/j.crma.2006.10.017 %G en %F CRMATH_2006__343_11-12_759_0
Lejmi, Mehdi. Strictly nearly Kähler 6-manifolds are not compatible with symplectic forms. Comptes Rendus. Mathématique, Tome 343 (2006) no. 11-12, pp. 759-762. doi : 10.1016/j.crma.2006.10.017. http://www.numdam.org/articles/10.1016/j.crma.2006.10.017/
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