| 叶薇薇,王安.一类Hartogs 域的Einstein-K\"{a}hler 度量和Kobayashi度量的比较定理[J].数学年刊A辑,2012,33(6):687~704 |
| 一类Hartogs 域的Einstein-K\"{a}hler 度量和Kobayashi度量的比较定理 |
| Comparison Theorem for Einstein-K¨ahler Metric and Kobayashi Metric on Hartogs Domain |
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| DOI： |
| 中文关键词: Einstein-K\"{a}hler
度量, Ricci 曲率, 全纯截曲率,比较定理 |
| 英文关键词:Einstein-K¨ahler metric, Ricci curvature, Holomorphic sectional
curvature, Comparison theorem |
| 基金项目:国家自然科学基金 (No.11071171)和北京自然科学基金(No.1082005) |
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| 中文摘要: |
| 研究了一类~Hartogs 域~$\widehat{\Omega }$, 得到了该域上~Einstein-K\"{a}hler
度量生成函数的隐式解和在某些参数情况下完备的~Einstein-K\"{a}hler
度量显式表达式, 且给出了该域上~Einstein-K\"{a}hler
度量和~Kobayashi 度量的比较定理. |
| 英文摘要: |
| The authors discuss a class of Hartogs domains denoted by $\widehat {\Omega }$
, and obtain the
implicit solution to the generating function about the Einstein-K¨ahler metric. To some
specific parameters, the explicit expression of the complete Einstein-K¨ahler metric is given.
Furthermore, the authors get the comparison theorem between Einstein-K¨ahler metric and
Kobayashi metric on this domain. |
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