Stability under deformations of Hermite-Einstein almost Kähler metrics

Lejmi, Mehdi

doi:10.5802/aif.2911

Stability under deformations of Hermite-Einstein almost Kähler metrics
[Stabilité sous déformations des métriques presque-kählériennes de Hermite-Einstein]

Lejmi, Mehdi ¹

¹ Université Libre de Bruxelles CP218 Département de Mathématiques Boulevard du Triomphe Bruxelles 1050, (Belgique)

Annales de l'Institut Fourier, Tome 64 (2014) no. 6, pp. 2251-2263.

Résumé
Abstract

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.

MR Zbl

DOI : 10.5802/aif.2911

Classification : 53C55, 53C15, 53D20
Keywords: Almost-Kähler geometry, extremal almost-Kähler metrics, constant Hermitian scalar curvature almost-Kähler metrics
Mot clés : Géométrie presque-kählérienne, métrique presque-kählériennes extrémales, métriques presque-kählériennes à courbure scalaire hermitienne constante

Affiliations des auteurs :

Lejmi, Mehdi ¹

¹ Université Libre de Bruxelles CP218 Département de Mathématiques Boulevard du Triomphe Bruxelles 1050, (Belgique)

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     title = {Stability under deformations of {Hermite-Einstein} almost {K\"ahler} metrics},
     journal = {Annales de l'Institut Fourier},
     pages = {2251--2263},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {64},
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     year = {2014},
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     url = {http://www.numdam.org/articles/10.5802/aif.2911/}
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Lejmi, Mehdi. Stability under deformations of Hermite-Einstein almost Kähler metrics. Annales de l'Institut Fourier, Tome 64 (2014) no. 6, pp. 2251-2263. doi : 10.5802/aif.2911. http://www.numdam.org/articles/10.5802/aif.2911/

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