Journal of Lie Theory

no. 3
Analyticity of Riemannian Exponential Maps on Diff(T)
Thomas Kappeler1; Enrique Loubet1; Peter Topalov2
1Mathematisches Institut, Universitaet Zuerich, Winterthurerstrasse 190, 8057 Zuerich, Switzerland
2Department of Mathematics, Northeastern University, 360 Huntington Avenue, Boston, MA 02115, U.S.A.
Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 481-503
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.
DOI: 10.5802/jolt.457
Classification: 22E65, 58B20, 17B68
Keywords: Group of diffeomorphisms, Riemannian exponential map, Camassa-Holm equation

Thomas Kappeler  1 ; Enrique Loubet  1 ; Peter Topalov  2

1 Mathematisches Institut, Universitaet Zuerich, Winterthurerstrasse 190, 8057 Zuerich, Switzerland
2 Department of Mathematics, Northeastern University, 360 Huntington Avenue, Boston, MA 02115, U.S.A. 
Thomas Kappeler; Enrique Loubet; Peter Topalov. Analyticity of Riemannian Exponential Maps on Diff(T). Journal of Lie Theory, Volume 17 (2007) no. 3, pp. 481-503. doi: 10.5802/jolt.457
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