Geodesic paths of circles in the plane

Author： Salvai Marcos  

Publisher： Springer Publishing Company

ISSN： 1139-1138

Source： Revista Matem??tica Complutense, Vol.24, Iss.1, 2011-01, pp. : 211-218

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Abstract

Let be the Fréchet space of all positively oriented embeddings of the circle in ℜ2 and let /∼ be the quotient of modulo orientation preserving diffeomorphisms of the circle. Let π:→/∼ be the canonical projection and let $mathcal{C}$ denote the space of all constant speed circles. We study geodesics in $mathcal{C}$ and $pi (mathcal{C})$ endowed with the Riemannian metrics induced from the canonical weak Riemannian metrics on and /∼, respectively. We also study the holonomy of closed paths in $pi (mathcal{C})$ .

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