Bergman local isometries are biholomorphisms

TL;DR

This paper proves that any proper holomorphic local isometry between bounded domains with Bergman metrics must be a biholomorphism, using a novel approach based on Information Geometry.

Contribution

It introduces a new method leveraging Information Geometry to establish that Bergman local isometries are biholomorphisms, advancing understanding of complex domain mappings.

Findings

Proper holomorphic local isometries are biholomorphisms.

New proof technique based on Information Geometry.

Strengthens the link between metric isometries and biholomorphic maps.

Abstract

We prove that a proper holomorphic local isometry between bounded domains with respect to the Bergman metrics is necessarily a biholomorphism. The proof relies on a new method grounded in Information Geometry theories.