Rigidity of proper holomorphic mappings between nonequidimensional bounded symmetric domains
Rigidity of proper holomorphic mappings between nonequidimensional bounded symmetric domains
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DOI：
10.1007/s002090100353
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发表时间：
2002-05
影响因子：
0.8
通讯作者：
Zhenhan Tu
中科院分区：
文献类型：
--
作者：
Zhenhan Tu
我们证明了从图到图的任何适当全纯映射必然是关于它们的Bergman度量的完全测地线等距嵌入，因此是直到它们的自同构的标准线性嵌入。本文的主要结果将通过对一类特殊的复测地线曲线在有界对称域上关于它们的Bergman度量的微分几何研究来证明。
We prove that any proper holomorphic mapping fromtois necessarily a totally geodesic isometric embedding with respect to their Bergman metrics and therefore is the standard linear embedding up to their automorphisms. The proof of the main result in this paper will be achieved by a differential-geometric study of a special class of complex geodesic curves on the bounded symmetric domains with respect to their Bergman metrics.