Self-dual almost-Kähler four manifolds

2023/11/29 by Inyoung Kim, Kim, Inyoung · 1 citation
Mathematics · #53C21 #53C25 #57K41 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2311.17672

openalex publication_date 2023/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify compact self-dual almost-Kähler four manifolds of positive type and zero type. In particular, using LeBrun's result, we show that any self-dual almost-Kähler metric on a manifold which is diffeomorphic to \mathbbCP₂ is the Fubini-Study metric up to rescaling. In case of negative type, we classify compact self-dual almost-Kähler four manifolds with J-invariant Ricci tensor.

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

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