Closed almost-K "ahler 4-manifolds of constant non-negative Hermitian\n holomorphic sectional curvature are K "ahler

2017/09/15 by Mehdi Lejmi, Lejmi, Mehdi, Markus Upmeier +1
Mathematics · #53B35 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1709.05210

openalex publication_date 2017/09/15 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We show that a closed almost K "ahler 4-manifold of globally constant\nholomorphic sectional curvature k\≥ 0 with respect to the canonical\nHermitian connection is automatically K "ahler. The same result holds for k<0\nif we require in addition that the Ricci curvature is J-invariant. The proofs\nare based on the observation that such manifolds are self-dual, so that\nChern-Weil theory implies useful integral formulas, which are then combined\nwith results from Seiberg--Witten theory.\n

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