Geodesic Flow on the Diffeomorphism Group of the circle

Abstract : 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.
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Commentarii Mathematici Helvetici, European Mathematical Society, 2003, 78, pp.787-804. 〈10.1007/s00014-003-0785-6〉
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Contributeur : Boris Kolev <>
Soumis le : samedi 13 novembre 2004 - 15:50:41
Dernière modification le : jeudi 11 octobre 2018 - 01:19:41

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Boris Kolev, Adrian Constantin. Geodesic Flow on the Diffeomorphism Group of the circle. Commentarii Mathematici Helvetici, European Mathematical Society, 2003, 78, pp.787-804. 〈10.1007/s00014-003-0785-6〉. 〈hal-00003261〉

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