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http://dx.doi.org/10.4134/BKMS.b160709

A CHARACTERIZATION OF THE HYPERBOLIC DISC AMONG CONSTANT WIDTH BODIES

Jeronimo-Castro, Jesus (Facultad de Ingenieria Universidad Autonoma de Queretaro)
Jimenez-Lopez, Francisco G. (Facultad de Ingenieria Universidad Autonoma de Queretaro)

Publication Information

Bulletin of the Korean Mathematical Society / v.54, no.6, 2017 , pp. 2053-2063 More about this Journal

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;

Citations & Related Records

Reference

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