Stability under deformations of Hermite-Einstein almost Kähler metrics

Lejmi, Mehdi

doi:10.5802/aif.2911

Cited by 7 publications

(1 citation statement)

References 14 publications

(20 reference statements)

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“…As we will see, this approach does not work so well in the almost-Kähler setting. In dimension 4, 'almost-Kähler potentials' have been used by Weinkove [48] in his study of the Calabi-Yau equation on almost-Kähler manifolds, and by Lejmi [26]. However, this method involves the use of pseudo-differential operators.…”

Section: Statement Of Resultsmentioning

confidence: 99%

Almost-Kähler smoothings of compact complex surfaces with $A_1$ singularities

Vernier

2020

Journal of Symplectic Geometry

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This paper is concerned with the existence of metrics of constant Hermitian scalar curvature on almost-Kähler manifolds obtained as smoothings of a constant scalar curvature Kähler orbifold, with A1 singularities. More precisely, given such an orbifold that does not admit nontrivial holomorphic vector fields, we show that an almost-Kähler smoothing (Mε, ωε) admits an almost-Kähler structure (Ĵε,ĝε) of constant Hermitian curvature. Moreover, we show that for ε > 0 small enough, the (Mε, ωε) are all symplectically equivalent to a fixed symplectic manifold (M ,ω) in which there is a surface S homologous to a 2-sphere, such that [S] is a vanishing cycle that admits a representant that is Hamiltonian stationary forĝε.

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Section: Statement Of Resultsmentioning

confidence: 99%

Almost-Kähler smoothings of compact complex surfaces with $A_1$ singularities

Vernier

2020

Journal of Symplectic Geometry

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Extremal K-contact metrics

Lejmi

Upmeier

2015

Math. Z.

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Abstract. Extending a result of He to the non-integrable case of K-contact manifolds, it is shown that transverse Hermitian scalar curvature may be interpreted as a moment map for the strict contactomorphism group. As a consequence, we may generalize the Sasaki-Futaki invariant to K-contact geometry and establish a number of elementary properties.Moreover, we prove that in dimension 5 certain deformation-theoretic results can be established also under weaker integrability conditions by exploiting the relationship between J-anti-invariant and self-dual 2-forms.

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Homogeneous almost-Kähler manifolds and the Chern–Einstein equation

Alekseevsky

Podestà

2019

Math. Z.

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Given a non compact semisimple Lie group G we describe all homogeneous spaces G/L carrying an invariant almost Kähler structure (ω, J). When L is abelian and G is of classical type, we classify all such spaces which are Chern-Einstein, i.e. which satisfy ρ = λω for some λ ∈ R, where ρ is the Ricci form associated to the Chern connection.2010 Mathematics Subject Classification. 53C25, 53C30.

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Stability under deformations of Hermite-Einstein almost Kähler metrics

Cited by 7 publications

References 14 publications

Almost-Kähler smoothings of compact complex surfaces with $A_1$ singularities

Almost-Kähler smoothings of compact complex surfaces with $A_1$ singularities

Extremal K-contact metrics

Homogeneous almost-Kähler manifolds and the Chern–Einstein equation

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