The automorphism group of a certain unbounded non-hyperbolic domain

TL;DR

This paper determines the automorphism group of a specific unbounded, non-hyperbolic domain called the Fock-Bargmann-Hartogs domain in complex space, expanding understanding of its symmetry properties.

Contribution

It explicitly characterizes the automorphism group of the Fock-Bargmann-Hartogs domain, a previously unstudied class of unbounded, non-hyperbolic domains.

Findings

Automorphism group explicitly determined

Provides new insights into symmetries of non-hyperbolic domains

Enhances understanding of complex domain automorphisms

Abstract

In this paper we determine the automorphism group of the Fock-Bargmann-Hartogs domain $D_{n,m}$ in $\mathbb{C}^n\times\mathbb{C}^m$ which is defined by the inequality ${\|\zeta\|}^2<e^{-\mu{\|z\|}^2}$.