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

Author: Gerard Misiolek
Journal: Proc. Amer. Math. Soc. 125 (1997), 935-940
MSC (1991): Primary 58D05; Secondary 35Q53
MathSciNet review: 1363431
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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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Additional Information

Gerard Misiolek
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556

Keywords: Diffeomorphism groups, KdV equation, conjugate points
Received by editor(s): October 11, 1995
Communicated by: Hal L. Smith
Article copyright: © Copyright 1997 American Mathematical Society