Commentarii Mathematici Helvetici

Full-Text PDF (241 KB) | Metadata | Table of Contents | CMH summary
Volume 78, Issue 4, 2003, pp. 787–804
DOI: 10.1007/s00014-003-0785-6

Published online: 2003-12-31

Geodesic flow on the diffeomorphism group of the circle

Adrian Constantin[1] and Boris Kolev[2]

(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