TWO THEOREMS ON THE FOCK-BARGMANN-HARTOGS DOMAINS

Abstract

In this paper, we prove two mutually independent theorems on the family of Fock-BargmannHartogs domains. Let D1 and D2 be two Fock-Bargmann-Hartogs domains in CN1 and CN2 , 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.