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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 $\widehat {{\cal D}}(S^1)$ 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 $\widehat {{\cal D}}(S^1)$.


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Additional Information

Gerard Misiolek
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: misiolek.1@nd.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03711-8
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