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

TL;DR

This paper constructs specific unbounded domains in complex n-space with finite-dimensional Bergman spaces, constant positive curvature Bergman metrics, and only linear automorphisms, expanding understanding of complex geometric structures.

Contribution

It introduces new unbounded domains with finite-dimensional Bergman spaces, constant curvature metrics, and linear automorphism groups, which were not previously known.

Findings

Bergman spaces are finite-dimensional on these domains.

Bergman metrics have constant sectional curvature 2.

Automorphism groups are restricted to linear mappings.

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.