Stability under deformations of Hermite-Einstein almost Kähler metrics
[Stabilité sous déformations des métriques presque-kählériennes de Hermite-Einstein]
Lejmi, Mehdi
Annales de l'Institut Fourier, Tome 64 (2014), p. 2251-2263 / Harvested from Numdam
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Sur une variété symplectique compacte de dimension 4, nous considérons une famille lisse de structures presque-complexes compatibles tel qu’en temps zéro, la métrique induite est presque-kählérienne de Hermite-Einstein avec une courbure scalaire hermitienne nulle ou négative. Nous prouvons, sous une certaine hypothèse, l’existence d’une famille lisse de structures presque-complexes, difféomorphe à chaque temps à la structure initiale et induisant une métrique à courbure scalaire hermitienne constante.

On a 4-dimensional compact symplectic manifold, we consider a smooth family of compatible almost-complex structures such that at time zero the induced metric is Hermite-Einstein almost-Kähler metric with zero or negative Hermitian scalar curvature. We prove, under certain hypothesis, the existence of a smooth family of compatible almost-complex structures, diffeomorphic at each time to the initial one, and inducing constant Hermitian scalar curvature metrics.

Publié le : 2014-01-01
DOI : https://doi.org/10.5802/aif.2911
Classification:  53C55,  53C15,  53D20
Mots clés: Géométrie presque-kählérienne, métrique presque-kählériennes extrémales, métriques presque-kählériennes à courbure scalaire hermitienne constante 
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     author = {Lejmi, Mehdi},
     title = {Stability under deformations of Hermite-Einstein almost K\"ahler metrics},
     journal = {Annales de l'Institut Fourier},
     volume = {64},
     year = {2014},
     pages = {2251-2263},
     doi = {10.5802/aif.2911},
     zbl = {06387338},
     mrnumber = {3331165},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2014__64_6_2251_0}
}

Lejmi, Mehdi. Stability under deformations of Hermite-Einstein almost Kähler metrics. Annales de l'Institut Fourier, Tome 64 (2014) pp. 2251-2263. doi : 10.5802/aif.2911. http://gdmltest.u-ga.fr/item/AIF_2014__64_6_2251_0/

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