TWO THEOREMS ON THE FOCK-BARGMANN-HARTOGS DOMAINS

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Abstract

In this paper, we prove two mutually independent theorems on the family of Fock-Bargmann-Hartogs domains. Let D₁ and D₂ be two Fock-Bargmann-Hartogs domains in C＾<N₁> and C＾<N₂>, 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.

Journal

  • Osaka Journal of Mathematics

    Osaka Journal of Mathematics 56 (4), 739-757, 2019-10

    Osaka University and Osaka City University, Departments of Mathematics

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