Classification of non-CSC extremal K\"{a}hler metrics on K-surfaces $S^2_{\{\alpha\}}$ and $S^2_{\{\alpha,\beta\}}$

Yingjie Meng; Zhiqiang Wei

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arXiv · 2407.07537

Classification of non-CSC extremal K\"{a}hler metrics on K-surfaces $S^2_{\{\alpha\}}$ and $S^2_{\{\alpha,\beta\}}$

Yingjie Meng·Zhiqiang Wei

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Abstract

We commonly refer to an extremal K\"{a}hler 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 $S^2_{\{\alpha\}}$ and $S^2_{\{\alpha,\beta\}}$.

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Yingjie Meng, Zhiqiang Wei. 2024-07-10. Classification of non-CSC extremal K\"{a}hler metrics on K-surfaces $S^2_{\{\alpha\}}$ and $S^2_{\{\alpha,\beta\}}$. https://arxiv.org/abs/2407.07537

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