Uniqueness Results for Bodies of Constant Width in the Hyperbolic Plane

TL;DR

This paper extends Santaló's approach to hyperbolic geometry, providing characterizations of disks among bodies with constant width, projections, or sections along geodesics.

Contribution

It offers new geometric characterizations of bodies of constant width in the hyperbolic plane, generalizing classical Euclidean results.

Findings

Disks characterized by constant width, projections, or sections in hyperbolic geometry.

New geometric criteria for identifying disks in the hyperbolic plane.

Extension of Santaló's approach to non-Euclidean settings.

Abstract

Following Santal\'{o}'s approach, we prove several characterizations of a disc among bodies of constant width, constant projections lengths, or constant section lengths on given families of geodesics.