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Springer, Annals of Global Analysis and Geometry, 2(31), p. 155-180, 2006

DOI: 10.1007/s10455-006-9042-8

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On geodesic exponential maps of the Virasoro group

Journal article published in 2006 by Adrian Constantin ORCID, Thomas Kappeler, Boris Kolev, Peter Topalov
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This paper is available in a repository.

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Abstract

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.