Stability under deformations of Hermite-Einstein almost Kähler metrics

Mehdi Lejmi[1]

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

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 6, page 2251-2263
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Lejmi, Mehdi. "Stability under deformations of Hermite-Einstein almost Kähler metrics." Annales de l’institut Fourier 64.6 (2014): 2251-2263. <http://eudml.org/doc/275507>.

@article{Lejmi2014,
abstract = {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.},
affiliation = {Université Libre de Bruxelles CP218 Département de Mathématiques Boulevard du Triomphe Bruxelles 1050, (Belgique)},
author = {Lejmi, Mehdi},
journal = {Annales de l’institut Fourier},
keywords = {Almost-Kähler geometry; extremal almost-Kähler metrics; constant Hermitian scalar curvature almost-Kähler metrics; almost-Kähler geometry},
language = {eng},
number = {6},
pages = {2251-2263},
publisher = {Association des Annales de l’institut Fourier},
title = {Stability under deformations of Hermite-Einstein almost Kähler metrics},
url = {http://eudml.org/doc/275507},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Lejmi, Mehdi
TI - Stability under deformations of Hermite-Einstein almost Kähler metrics
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 6
SP - 2251
EP - 2263
AB - 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.
LA - eng
KW - Almost-Kähler geometry; extremal almost-Kähler metrics; constant Hermitian scalar curvature almost-Kähler metrics; almost-Kähler geometry
UR - http://eudml.org/doc/275507
ER -

References

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