Geodesic paths of circles in the plane

Abstract

Let E be the Fréchet space of all positively oriented embeddings of the circle in R^2 and let E/¬ be the quotient of E modulo orientation preserving diffeomorphisms of the circle. Let p : E --> E/¬ be the canonical projection and let C denote the space of all constant speed circles. We study geodesics in C and p(C) endowed with the Riemannian metrics induced from the canonical weak Riemannian metrics on E and E/¬, respectively. We also study the holonomy of closed paths in p(C).