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| 摘要: |
| 本文考虑了等维Cartan-Hartogs域之间的全纯映射.如果Cartan-Hartogs域ΩBm(μ)不是球,则它上面存在一函数X使得它在ΩBm(μ)的任一全纯自同构作用下不变.通过直接计算得到:如果等维Cartan-Hartogs域间的全纯映射F保持函数X不变,则F必是双全纯映射.由此可得如果Cartan-Hartogs域ΩBm(μ)不是球,ΩBm(μ)的全纯自映射是自同构的充要条件是F保持函数X不变. |
| 关键词: 双全纯映射 有界对称域 Cartan-Hartogs域 |
| DOI： |
| 分类号:O174.56 |
| 基金项目:The research was supported by the Scientific Research Fund of SiChuan Provincial Education Department (15ZA0284). |
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| A CHARACTERIZATION OF THE BIHOLOMORPHISMS BETWEEN EQUIDIMENSIONAL CARTAN-HARTOGS DOMAINS |
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FENG Zhi-ming
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| Abstract: |
| The holomorphic mappings F between equidimensional Cartan-Hartogs domains are considered.If a Cartan-Hartogs domain ΩBm(μ) is not the unit ball,then there is a function X on ΩBm(μ) such that any holomorphic automorphism of ΩBm(μ) leaves the function X on ΩBm(μ) invariant.By direct calculations,we obtain that if a holomorphic mapping F between equidimensional Cartan-Hartogs domains leaves the functions X invariant,then F must be a biholomorphism.As a consequence of our result,if a Cartan-Hartogs domain ΩBm(μ) is not the unit ball,then,for any holomorphic self-mapping F on ΩBm(μ),we have that F is a holomorphic automorphism of ΩBm(μ) if and only if F leaves the function X on ΩBm(μ) invariant. |
| Key words: biholomorphic mappings bounded symmetric domains Cartan-Hartogs domains |
