Bergman local isometries are biholomorphisms

In this paper, 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.

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Publication Details

Journal
International Journal of Mathematics
Published
2025-10-31
DOI
https://doi.org/10.1142/s0129167x26500059
Primary Topic
Geometry and complex manifolds
Type
article
Field-Weighted Citation Impact
0.00
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article

Bergman local isometries are biholomorphisms

Jihun Yum
International Journal of Mathematics
Geometry and complex manifolds
article

Bergman local isometries are biholomorphisms

Jihun Yum
article en

Abstract

In this paper, 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.

International Journal of MathematicsVol. 37(01)
Jeonbuk National University (KR)
Openalex Percentile: Top 62%
Geometry and complex manifolds
DOISourceOpenAlex
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Bergman local isometries are biholomorphisms — Jihun Yum · International Journal of Mathematics (2025) | TGRS Research Map | TGRS