Abstract
We study the geometry of a right invariant metric on a central extension D ^ ( S 1 ) \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 D ^ ( S 1 ) \widehat {\mathcal {D}}(S^1) .
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