Commentarii Mathematici Helvetici
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Published online: 2003-12-31
Geodesic flow on the diffeomorphism group of the circleAdrian Constantin and Boris Kolev (1) King's College London, UK
(2) Université de Provence, Marseille, France
We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to prove infinite-dimensional counterparts of results from classical Riemannian geometry: the Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of the geodesics holds.
Keywords: Geodesic flow, diffeomorphism group of the circle
Constantin Adrian, Kolev Boris: Geodesic flow on the diffeomorphism group of the circle. Comment. Math. Helv. 78 (2003), 787-804. doi: 10.1007/s00014-003-0785-6