Einstein Manifolds, Self-Dual Weyl Curvature, and Conformally Kaehler Geometry

2019/08/05 by Claude LeBrun, LeBrun, Claude
Mathematics · Physics and Astronomy · #14J26 #32J15 #53C25 (Primary) #53C55 (Secondary) #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1908.01881

openalex publication_date 2019/08/05 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

Peng Wu recently announced a beautiful characterization of conformally Kaehler, Einstein metrics of positive scalar curvature on compact oriented 4-manifolds via the condition det (W⁺) > 0. In this note, we buttress his claim by providing an entirely different proof of his result. We then present further consequences of our method, which builds on techniques previously developed in (LeBrun 2015).

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