Stability under deformations of extremal almost-K "ahler metrics in\n dimension 4

2010/04/21 by Mehdi Lejmi, Lejmi, Mehdi · 1 citation
Mathematics · Medicine · #53B35 #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Pelvic and Acetabular Injuries

paper · pdf · doi:10.48550/arxiv.1004.3747

openalex publication_date 2010/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a path of almost-K "ahler metrics compatible with a fixed symplectic\nform on a compact 4-manifold such that at time zero the almost-K "ahler metric\nis an extremal K "ahler one, we prove, for a short time and under a certain\nhypothesis, the existence of a smooth family of extremal almost-K "ahler\nmetrics compatible with the same symplectic form, such that at each time the\ninduced almost-complex structure is diffeomorphic to the one induced by the\npath.\n

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