On isometric minimal immersion of a singular non-CSC extremal Kahler metric into 3-dimensional space forms

2021/12/31 by Zhiqiang Wei, Wei, Zhiqiang, Yingyi Wu +1
Mathematics · Physics and Astronomy · #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.2112.15526

openalex publication_date 2021/12/31 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

On any compact Riemann surface there always exists a singular non-CSC (constant scalar curvature) extremal Kahler metric which is called a non-CSC HCMU (the Hessian of the Curvature of the Metric is Umbilical) metric. In this paper, by moving frames, we show that any non-CSC HCMU metric can not be isometrically minimal immersed into 3-dimensional real space forms even locally. In general, any non-CSC HCMU metric can not be isometrically immersed into 3-dimensional real space forms with constant mean curvature (CMC).

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