Inscriptions in non-Euclidean Geometries

Abstract

Abstract We show how inscription problems in the plane can be generalised to Riemannian surfaces of constant curvature. We then use ideas from symplectic and Riemannian geometry to prove these generalised versions for smooth Jordan curves in the hyperbolic plane, and we prove a rectangular inscription theorem for smooth Jordan curves on the two sphere that do not intersect their antipodal.