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Article Dans Une Revue Annals of Global Analysis and Geometry Année : 2007

On geodesic exponential maps of the Virasoro group

Résumé

We study the geodesic exponential maps corresponding to Sobolev type right-invariant (weak) Riemannian metrics μ(k) (k≥ 0) on the Virasoro group Vir and show that for k≥ 2, but not for k = 0,1, each of them defines a smooth Fréchet chart of the unital element e ∈Vir. In particular, the geodesic exponential map corresponding to the Korteweg–de Vries (KdV) equation (k = 0) is not a local diffeomorphism near the origin.

Dates et versions

hal-00130915 , version 1 (14-02-2007)

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Boris Kolev, Thomas Kappeler, Adrian Constantin, Peter Topalov. On geodesic exponential maps of the Virasoro group. Annals of Global Analysis and Geometry, 2007, 31 (2), p. : 155--180. ⟨10.1007/s10455-006-9042-8⟩. ⟨hal-00130915⟩
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