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.

15 pages

References in corpus (1)

• An integrable shallow water equation with peaked solitons

Cited by in corpus (2)

• Two-component higher order Camassa-Holm systems with fractional inertia operator: a geometric approach
• Smoothness of the flow map for low-regularity solutions of the Camassa-Holm equations