Representation of Curves of Constant Width in the Hyperbolic Plane

Abstract

If γ is a curve of constant width in the hyperbolic plane H2, and l is a diameter of γ, the track function x(θ) gives the coordinate of the point of intersection l(x(θ)) of l with the diameter of γ that makes an angle θ with l. We show that x(θ) determines the shape of γ up to the choice of a constant; this provides a representation of all curves of… (More)

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