The automorphism group of a certain unbounded non-hyperbolic domain

In this paper we determine the automorphism group of the Fock–Bargmann–Hartogs domain _Dn,m$D_{n,m}$ in Cⁿ×C^m${\mathbb{C}}^n\times {\mathbb{C}}^m$ which is defined by the inequality ‖ζ‖²−μ‖z‖²${\Vert \zeta \Vert }^2<e^{-\mu {\Vert z\Vert }^2}$.