Journal of Lie Theory 17 (2007), No. 3, 481--503
Copyright Heldermann Verlag 2007
Analyticity of Riemannian Exponential Maps on Diff(T)
Thomas Kappeler
Mathematisches Institut, Universitaet Zuerich, Winterthurerstrasse 190, 8057 Zuerich, Switzerland
tk@math.unizh.ch
Enrique Loubet
Mathematisches Institut, Universitaet Zuerich, Winterthurerstrasse 190, 8057 Zuerich, Switzerland
loubet@math.unizh.ch
Peter Topalov
Department of Mathematics, Northeastern University, 360 Huntington Avenue, Boston, MA 02115, U.S.A.
p.topalov@neu.edu
We study the exponential maps induced by Sobolev type right-invariant (weak) Riemannian metrics of order k (greater or equal to 1) on the Lie group of smooth, orientation preserving diffeomorphisms of the circle. We prove that each of them defines an analytic Fréchet chart of the identity.
Keywords: Group of diffeomorphisms, Riemannian exponential map, Camassa-Holm equation.
MSC: 22E65, 58B20, 17B68
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