Almost-Kähler four manifolds with harmonic self-dual Weyl curvature

2023/11/28 by Inyoung Kim, Kim, Inyoung · 1 citation
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.2311.16729

Abstract

We show that a compact almost-Kähler four manifold (M, g, ω) with harmonic self-dual Weyl curvature and constant scalar curvature is Kähler if c₁⋅ω≥ 0. We also prove an integral curvature inequality for compact almost-Kähler four manifolds with harmonic self-dual Weyl curvature.

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• Pinched self-dual Weyl curvature on Einstein four-manifolds

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