Comptes Rendus
no. 13-14
Analytic Geometry
A Note on small deformations of balanced manifolds
[Une Note sur les petites déformations des variétés équilibrées]

Présenté par : Jean-Pierre Demailly

Jixiang Fu1 ; Shing-Tung Yau2
1 Institute of Mathematics, Fudan University, Shanghai 200433, China
2 Department of Mathematics, Harvard University, Cambridge, MA 02138, USA
Comptes Rendus. Mathématique, Volume 349 (2011) no. 13-14, pp. 793-796.

Dans cette Note nous montrons que, sous une condition plus faible que le lemme du ∂∂¯, lʼexistence de métriques équilibrées est préservée par des petites déformations. Cette condition affaiblie est satisfaite par lʼespace des twisteurs sur une variété différentielle de dimension 4, compacte et auto-duale.

In this Note we prove that, under a weaker condition than the ∂∂¯-lemma, the existence of balanced metrics is preserved under small deformations. This weaker condition is satisfied on the twistor space over a compact self-dual four manifold.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.06.023
Jixiang Fu 1 ; Shing-Tung Yau 2

1 Institute of Mathematics, Fudan University, Shanghai 200433, China
2 Department of Mathematics, Harvard University, Cambridge, MA 02138, USA 
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Jixiang Fu; Shing-Tung Yau. A Note on small deformations of balanced manifolds. Comptes Rendus. Mathématique, Volume 349 (2011) no. 13-14, pp. 793-796. doi : 10.1016/j.crma.2011.06.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.06.023/

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