Annals of Global Analysis and Geometry

, Volume 41, Issue 4, pp 461–472 | Cite as

Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation

  • Martin Bauer
  • Martins Bruveris
  • Philipp Harms
  • Peter W. Michor
Article

Abstract

The Virasoro-Bott group endowed with the right-invariant L2-metric (which is a weak Riemannian metric) has the KdV-equation as geodesic equation. We prove that this metric space has vanishing geodesic distance.

Keywords

Diffeomorphism group Virasoro group Geodesic distance 

Mathematics Subject Classification (2000)

Primary 35Q53 58B20 58D05 58D15 58E12 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Martin Bauer
    • 1
  • Martins Bruveris
    • 2
  • Philipp Harms
    • 1
  • Peter W. Michor
    • 1
  1. 1.Fakultät für MathematikUniversität WienWienAustria
  2. 2.Department of MathematicsImperial CollegeLondonUK

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