Osaka Journal of Mathematics

Two theorems on the Fock-Bargmann-Hartogs domains

Akio Kodama and Satoru Shimizu

Full-text: Open access

Abstract

In this paper, we prove two mutually independent theorems on the family of Fock-Bargmann-Hartogs domains. Let $D_1$ and $D_2$ be two Fock-Bargmann-Hartogs domains in $\mathbb{C}^{N_1}$ and $\mathbb{C}^{N_2}$, respectively. In Theorem 1, we obtain a complete description of an arbitrarily given proper holomorphic mapping between $D_1$ and $D_2$ in the case where $N_1 = N_2$. Also, we shall give a geometric interpretation of Theorem 1. And, in Theorem 2, we determine the structure of $\text{Aut}(D_1\times D_2)$ using the data of $\text{Aut}(D_1)$ and $\text{Aut}(D_2)$ for arbitrary $N_1$ and $N_2$.

Article information

Source
Osaka J. Math., Volume 56, Number 4 (2019), 739-757.

Dates
First available in Project Euclid: 21 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1571623220

Mathematical Reviews number (MathSciNet)
MR4020635

Subjects
Primary: 32A07: Special domains (Reinhardt, Hartogs, circular, tube)
Secondary: 32M05: Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]

Citation

Kodama, Akio; Shimizu, Satoru. Two theorems on the Fock-Bargmann-Hartogs domains. Osaka J. Math. 56 (2019), no. 4, 739--757. https://projecteuclid.org/euclid.ojm/1571623220


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