A characterization of the hyperbolic disc among constant width bodies
Bull. Korean Math. Soc. 2017 Vol. 54, No. 6, 2053-2063
https://doi.org/10.4134/BKMS.b160709
Published online November 30, 2017
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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