Classification of non-CSC extremal Kähler metrics on K-surfaces S²_\α\ and S²_\α,β\

2024/07/10 by Yingjie Meng, Zhiqiang Wei, Meng, Yingjie +1
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2407.07537

openalex publication_date 2024/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We commonly refer to an extremal Kähler metric with finitely many singularities on a compact Riemann surface as an HCMU (Hessian of the Curvature of the Metric is Umbilical) metric. In this study, we specifically classify non-CSC HCMU metrics on the K-surfaces S²_\α\ and S²_\α,β\.

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