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We show that certain right-invariant metrics endow the infinite-dimensionalLie group of all smooth orientation-preserving diffeomorphisms of the circlewith a Riemannian structure. The study of the Riemannian exponential map allowsus to prove infinite-dimensional counterparts of results from classicalRiemannian geometry: the Riemannian exponential map is a smooth localdiffeomorphism and the length-minimizing property of the geodesics holds.Comment: 15 page

Hk Metrics on the Diffeomorphism Group of the Circle