等维Cartan-Hartogs域双全纯映射的特征（英文）  

A CHARACTERIZATION OF THE BIHOLOMORPHISMS BETWEEN EQUIDIMENSIONAL CARTAN-HARTOGS DOMAINS

作　　者：冯志明[1] 

机构地区：[1]乐山师范学院数学与信息科学学院

出　　处：《数学杂志》2015年第4期841-854,共14页Journal of Mathematics

基　　金：supported by the Scientific Research Fund of Si Chuan Provincial Education Department(15ZA0284)

摘　　要：本文考虑了等维Cartan-Hartogs域之间的全纯映射.如果Cartan-Hartogs域ΩB(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CartanmHartogs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ΩB(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 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 ofΩBm（μ） if and only if F leaves the function X on ΩBm（μ） invariant.

关 键 词：双全纯映射 有界对称域 CARTAN-HARTOGS域 

分 类 号：O174.56[理学—数学]