Unbounded Reinhardt domains with finite-dimensional Bergman spaces in $\C^n$

Abstract

In this paper, we construct unbounded domains in $\C^n$ ($n\geq 2$), whose Bergman spaces are nontrivial and finite-dimensional. We further show that the Bergman metrics on these domains have positive constant sectional curvature equal to $2$, and that their holomorphic automorphism groups consist only of linear mappings.