Hk metrics on the group of diffeomorphisms of the circle

Boris Kolev (1) , Adrian Constantin (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 Department of Mathematics [Lund University]

Each Hk inner product, endows the diffeomorphism group of the circle with a Riemannian structure. For an integer k greater than 1, the Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of geodesics holds.

Mots clés: Geodesic flows; Hydrodynamics

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Boris Kolev, Adrian Constantin. Hk metrics on the group of diffeomorphisms of the circle. Journal of Nonlinear Mathematical Physics, 2003, 10, pp.424-430. ⟨10.2991/jnmp.2003.10.4.1⟩. ⟨hal-00003270⟩