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Revista Matemática Complutense

, Volume 24, Issue 1, pp 211–218 | Cite as

Geodesic paths of circles in the plane

  • Marcos SalvaiEmail author
Article

Abstract

Let ℰ be the Fréchet space of all positively oriented embeddings of the circle in ℝ2 and let ℰ/ be the quotient of ℰ modulo orientation preserving diffeomorphisms of the circle. Let π:ℰ→ℰ/ 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 ℰ and ℰ/, respectively. We also study the holonomy of closed paths in \(\pi (\mathcal{C})\).

Keywords

Manifold of embeddings Geodesic Holonomy 

Mathematics Subject Classification (2000)

58D15 58B20 53C22 53C29 

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Copyright information

© Revista Matemática Complutense 2010

Authors and Affiliations

  1. 1.FaMAF-CIEMCórdobaArgentina

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