fock-bargmann-hartogs定域上的两个定理

Pub Date : 2019-10-01 DOI:10.18910/73626

A. Kodama, S. Shimizu

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引用次数: 1

摘要

本文证明了Fock-BargmannHartogs定域族上的两个相互独立的定理。设D1和D2分别为CN1和CN2中的两个Fock-Bargmann-Hartogs结构域。在定理1中，我们得到了当N1 = N2时，D1与D2之间任意给定的真全纯映射的完整描述。同时，我们将给出定理1的几何解释。在定理2中，我们利用任意N1和N2下的Aut(D1)和Aut(D2)的数据确定了Aut(D1 × D2)的结构。

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TWO THEOREMS ON THE FOCK-BARGMANN-HARTOGS DOMAINS

In this paper, we prove two mutually independent theorems on the family of Fock-BargmannHartogs domains. Let D1 and D2 be two Fock-Bargmann-Hartogs domains in CN1 and CN2 , respectively. In Theorem 1, we obtain a complete description of an arbitrarily given proper holomorphic mapping between D1 and D2 in the case where N1 = N2. Also, we shall give a geometric interpretation of Theorem 1. And, in Theorem 2, we determine the structure of Aut(D1 × D2) using the data of Aut(D1) and Aut(D2) for arbitrary N1 and N2.

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