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Geodesic Flow on the Diffeomorphism Group of the circle

Adrian Constantin·Boris Kolev
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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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Adrian Constantin, Boris Kolev. 2003-05-07. Geodesic Flow on the Diffeomorphism Group of the circle. https://doi.org/10.2991/jnmp.2003.10.4.1

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