Classification of Proper Holomorphic Mappings between Hartogs Domains over Homogeneous Siegel Domains  

作　　者：Lei WANG 

机构地区：[1]School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第11期2259-2274,共16页数学学报（英文版）

基　　金：the National Natural Science Foundation of China(Grant Nos.11801187,11871233 and 11871380)。

摘　　要：The Hartogs domain over homogeneous Siegel domain D_(N,s)(s>0)is defined by the inequality■,where D is a homogeneous Siegel domain of typeⅡ,(z,ζ)∈D×C~N and KD(z,z)is the Bergman kernel of D.Recently,Seo obtained the rigidity result that proper holomorphic mappings between two equidimensional domains D_(N,s)and D'_(N',s')are biholomorphisms for N≥2.In this article,we find a counter-example to show that the rigidity result is not true for D_(1,s)and obtain a classification of proper holomorphic mappings between D_(1,s)and D'_(1,s').

关 键 词：Hartogs domains homogeneous Siegel domain of typeⅡ proper holomorphic mappings AUTOMORPHISMS 

分 类 号：O174.5[理学—数学]