ON PROPER HOLOMORPHIC MAPPINGS BETWEEN TWO EQUIDIMENSIONAL FBH-TYPE DOMAINS

摘要

We introduce a new class of domains D-n,D-m (mu, p), called FBH-type domains, in C-n x C-m, where 0 < mu is an element of R and p is an element of N. In the special case of p = 1, these domains are just the Fock-Bargmann-Hartogs domains D-n,D-m (mu) in C-n x C-m introduced by Yamamori. In this paper we obtain a complete description of an arbitrarily given proper holomorphic mapping between two equidimensional FBH-type domains. In particular, we prove that the holomorphic automorphism group Aut(D-n,D-m (mu, p)) of any FBH-type domain D-n,D-m(mu, p) with p not equal 1 is a Lie group isomorphic to the compact connected Lie group U (n) x U(m). This tells us that the structure of Aut(D-n,D-m (mu, p)) with p not equal 1 is essentially different from that of Aut(D-n,D-m (mu)).