Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2016.08.31
  • Accepted : 2017.02.13
  • Published : 2017.11.30
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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.

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References

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