{"title":"Classification of non-CSC extremal Kähler metrics on K-surfaces $$S^2_{\\{\\alpha \\}}$$ and $$S^2_{\\{\\alpha ,\\beta \\}}$$","authors":"Yingjie Meng, Zhiqiang Wei","doi":"10.1007/s00208-024-02967-w","DOIUrl":null,"url":null,"abstract":"<p>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 <span>\\(S^2_{\\{\\alpha \\}}\\)</span> and <span>\\(S^2_{\\{\\alpha ,\\beta \\}}\\)</span>.</p>","PeriodicalId":18304,"journal":{"name":"Mathematische Annalen","volume":"141 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Annalen","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00208-024-02967-w","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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 \(S^2_{\{\alpha ,\beta \}}\).
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.