等维Cartan-Hartogs域双全纯映射的特征

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。%The holomorphic mappings F between equidimensional Cartan-Hartogs domains are considered. If a Cartan-Hartogs domainΩBm (µ) is not the unit ball, then there is a function X onΩBm (µ) such that any holomorphic automorphism ofΩBm (µ) leaves the function X onΩBm (µ) invariant. By direct calculations, we obtain that if a holomorphic mapping F between equidimen-sional Cartan-Hartogs domains leaves the functions X invariant, then F must be a biholomorphism. As a consequence of our result, if a Cartan-Hartogs domainΩBm (µ) is not the unit ball, then, for any holomorphic self-mapping F on ΩBm (µ), we have that F is a holomorphic automorphism ofΩBm (µ) if and only if F leaves the function X onΩBm (µ) invariant.