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

In this paper, we construct unbounded domains in ${\text{C}}^n$ ($n\ge 2$), 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.