两个等维fbh型域间的真全纯映射

IF 0.6 4区数学 Q3 MATHEMATICS

Kyushu Journal of Mathematics Pub Date : 2020-01-01 DOI:10.2206/kyushujm.74.149

A. Kodama

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引用次数: 0

摘要

我们在Cn × Cm中引入了一类新的域Dn,m(μ， p)，称为fbh型域，其中0< μ∈R, p∈n。在p = 1的特殊情况下，这些域正是Yamamori在Cn × Cm中引入的Fock-Bargmann-Hartogs域Dn,m(μ)。本文给出了两个等维fbh型域之间任意给定的固有全纯映射的完整描述。特别地，我们证明了任意fbh型定义域Dn,m(μ， p)且p 6= 1的全纯自同构群Aut(Dn,m(μ， p))是紧连通李群U (n)×U (m)同构的李群，这说明了当p 6= 1时Aut(Dn,m(μ， p))的结构与Aut(Dn,m(μ))的结构本质上是不同的。

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ON PROPER HOLOMORPHIC MAPPINGS BETWEEN TWO EQUIDIMENSIONAL FBH-TYPE DOMAINS

We introduce a new class of domains Dn,m(μ, p), called FBH-type domains, in Cn × Cm , where 0< μ ∈ R and p ∈ N. In the special case of p = 1, these domains are just the Fock–Bargmann–Hartogs domains Dn,m(μ) in Cn × Cm introduced by Yamamori. In this paper we obtain a complete description of an arbitrarily given proper holomorphic mapping between two equidimensional FBH-type domains. In particular, we prove that the holomorphic automorphism group Aut(Dn,m(μ, p)) of any FBH-type domain Dn,m(μ, p) with p 6= 1 is a Lie group isomorphic to the compact connected Lie group U (n)×U (m). This tells us that the structure of Aut(Dn,m(μ, p)) with p 6= 1 is essentially different from that of Aut(Dn,m(μ)).

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来源期刊

Kyushu Journal of Mathematics 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total. More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.