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. MichorEmail author


The Virasoro-Bott group endowed with the right-invariant L 2-metric (which is a weak Riemannian metric) has the KdV-equation as geodesic equation. We prove that this metric space has vanishing geodesic distance.


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
    Email author
  1. 1.Fakultät für MathematikUniversität WienWienAustria
  2. 2.Department of MathematicsImperial CollegeLondonUK

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