Canonical metrics on generalized Cartan-Hartogs domains

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• 作者：Yihong Hao
• 刊名：Chinese Annals of Mathematics - Series B
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：37
• 期：3
• 页码：357-366
• 全文大小：196 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Applications of Mathematics
  Chinese Library of Science
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1860-6261
• 卷排序：37

文摘

In this paper, the author considers a class of bounded pseudoconvex domains, i.e., the generalized Cartan-Hartogs domains Ω(μ, m). The first result is that the natural Kähler metric gΩ(μ, m) of Ω(μ, m) is extremal if and only if its scalar curvature is a constant. The second result is that the Bergman metric, the Kähler-Einstein metric, the Carathéodary metric, and the Koboyashi metric are equivalent for Ω(μ, m).KeywordsCanonical metricExtremal metricComparison theoremGeneralized Cartan-Hartogs domains