Geodesic Flow on the Diffeomorphism Group of the circle

Details Geodesic Flow on the Diffeomorphism Group of the circle Geodesic Flow on the Diffeomorphism Group of the circle

2003-05-07

arxiv.org/abs/math-ph/0305013v1

Comment. Math. Helv. 78 no 4, pp. 787--804 (2003)

Physics

Mathematical Physics

15 pages

Scientific paper

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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