中山大学学报自然科学版 ›› 2011, Vol. 50 ›› Issue (6): 20-22.

• 研究论文 • 上一篇    下一篇

Cartan-Hartogs域上K-hler-Einstein度量的显表达式问题

邓义华,肖 娟,阳志锋   

  1. (衡阳师范学院数学与计算科学系,湖南 衡阳 421008)
  • 收稿日期:2011-03-07 修回日期:1900-01-01 出版日期:2011-11-25 发布日期:2011-11-25

Explicit Formula of Kähler-Einstein Metric on CartanHartogs Domains

DENG Yihua, XIAO Juan, YANG Zhifeng   

  1. (Department of Mathematic and Computing Sciences,Hengyang Normal University,Hengyang 421008,China)
  • Received:2011-03-07 Revised:1900-01-01 Online:2011-11-25 Published:2011-11-25

摘要:

讨论了Cartan-Hartogs域上Kähler-Einstein 度量的显表达式以及该度量与Bergman度量的等价性问题。得到了Cartan-Hartogs域上K-hler-Einstein度量显表达式的统一公式。运用该公式与连续函数的性质以及Bergman度量显表达式的一个统一公式,得到了这类域上K-hler-Einstein度量和Bergman度量等价性的统一证明。

关键词: Cartan-Hartogs域, Kä, hler-Einstein 度量, Bergman度量, 显表达式

Abstract: The explicit formula of Kähler-Einstein metric and the equivalence of the Kähler-Einstein metric and the Bergman metric on Cartan-Hartogs domains are discussed. A unified explicit formula of Kähler-Einstein metrics on Cartan-Hartogs domains is given. Using this formula and a nature of continuous functions and the unified explicit formula of Bergman metrics, a unified proof of the equivalence of the Kähler-Einstein metric and the Bergman metric on Cartan-Hartogs domains is obtained.

Key words: Cartan-Hartogs domain, Kä, hler-Einstein metric, Bergman metric, explicit formula

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