Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(6): 2053-2063

Online first article July 26, 2017      Printed November 30, 2017

https://doi.org/10.4134/BKMS.b160709

Copyright © The Korean Mathematical Society.

A characterization of the hyperbolic disc among constant width bodies

Jes\'us Jer\'onimo-Castro, Francisco G. Jimenez-Lopez

Universidad Aut\'onoma de Quer\'etaro, Universidad Aut\'onoma de Quer\'etaro

Abstract

In this paper we prove a condition under which a hyperbolic starshaped set has a center of hyperbolic symmetry. We also give the definition of isometric diameters for a hyperbolic convex set, which behave similar to affine diameters for Euclidean convex sets. Using this concept, we give a definition of constant hyperbolic width and we prove that the only hyperbolic sets with constant hyperbolic width and with a hyperbolic center of symmetry are hyperbolic discs.

Keywords: constant width, hyperbolic convex set, centrally symmetric set

MSC numbers: 51M09

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