K 曲面 $$S^2_{\{alpha \}}$ 和 $$S^2_{\{alpha ,\beta \}}$ 上的非 CSC 极值凯勒度量的分类

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-08-27 DOI:10.1007/s00208-024-02967-w

Yingjie Meng, Zhiqiang Wei

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引用次数: 0

摘要

我们通常把在紧凑黎曼曲面上具有有限多个奇点的极值凯勒度量称为度量，其中度量曲率的赫西阿斯是伞状的，称为 HCMU 度量。在这项研究中，我们特别对 K 曲面 $S^2_{\{alpha \}}\ 和 \(S^2_{\{alpha ,\beta \}}$ 上的非 CSC HCMU 度量进行了分类。）

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

We commonly refer to an extremal Kähler metric with finitely many singularities on a compact Riemann surface as a metric where the Hessian of the curvature of the Metric is Umbilical, known as an HCMU 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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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.