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 CN 1 and CN 2, 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.
|Number of pages||19|
|Journal||Osaka Journal of Mathematics|
|Publication status||Published - 2019 Oct|
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