Rigidity of the holomorphic automorphism of the generalized Fock-Bargmann-Hartogs domains
Ting Guo, Zhiming Feng, Enchao Bi (2021)
Czechoslovak Mathematical Journal
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We study a class of typical Hartogs domains which is called a generalized Fock-Bargmann-Hartogs domain . The generalized Fock-Bargmann-Hartogs domain is defined by inequality , where . In this paper, we will establish a rigidity of its holomorphic automorphism group. Our results imply that a holomorphic self-mapping of the generalized Fock-Bargmann-Hartogs domain becomes a holomorphic automorphism if and only if it keeps the function invariant.