A characterization of the hyperbolic disc among constant width bodies

摘要

In this paper we prove a condition under which a hyperbolicstarshaped set has a center of hyperbolic symmetry. We also give thedefinition of isometric diameters for a hyperbolic convex set, which behavesimilar to affine diameters for Euclidean convex sets. Using this concept,we give a definition of constant hyperbolic width and we prove that theonly hyperbolic sets with constant hyperbolic width and with a hyperboliccenter of symmetry are hyperbolic discs.