An Integrability Theorem for Almost-Kähler Structures using J-anti-invariant Two-Forms on Four-Manifolds

2015/07/01 by Mehdi Lejmi, Lejmi, Mehdi, Markus Upmeier +1
Mathematics · #53B35 #53C55 #53D05 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1507.00282

openalex publication_date 2015/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a new criterion for a compatible almost complex structure on a symplectic four-manifold to be integrable and hence Kähler. Our main theorem shows that the existence of three linearly independent closed J-anti-invariant two-forms implies the integrability of the almost complex structure. This proves the conjecture of Draghici-Li-Zhang in the almost-Kähler case

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