Conjugate points in the Bott-Virasoro group and the KdV equation

Misiolek, Gerard

doi:10.1090/S0002-9939-97-03711-8

Conjugate points in the Bott-Virasoro group and the KdV equation
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Proc. Amer. Math. Soc. 125 (1997), 935-940 Request permission

Abstract:

We study the geometry of a right invariant metric on a central extension $\widehat {\mathcal {D}}(S^1)$ of the diffeomorphism group of a circle (the Bott-Virasoro group) introduced by Ovsienko and Khesin. We obtain an expression for the curvature tensor of this metric and apply it to find conjugate points in $\widehat {\mathcal {D}}(S^1)$.

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