Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2020; 57(6): 1335-1345

Online first article January 9, 2020      Printed November 1, 2020

https://doi.org/10.4134/JKMS.j190640

Copyright © The Korean Mathematical Society.

A certain K\"ahler potential of the Poincar\'e metric and its characterization

Young-Jun Choi, Kang-Hyurk Lee, Sungmin Yoo

Pusan National University; Gyeongsang National University; Institute for Basic Science (IBS)

Abstract

We will show a rigidity of a K\"ahler potential of the Poincar\'e metric with a constant length differential.

Keywords: The Poincar\'e metric, K\"ahler hyperbolicity

MSC numbers: 32Q15, 32M25, 30F45

Supported by: The research of first and second named authors was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government (No. 2018R1C1B3005963, No. NRF-2019R1F1A1060891). The last named author was supported by IBS-R003-D1, Institute for Basic Science in Korea

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