Geodesic flow on the diffeomorphism group of the circle

Adrian Constantin, B Kolev

Research output: Contribution to journalArticlepeer-review

300 Citations (SciVal)


We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to prove infinite-dimensional counterparts of results from classical Riemannian geometry: the Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of the geodesics holds.
Original languageEnglish
Pages (from-to)787-804
JournalCommentar II Mathematici Helvetici
Issue number4
Publication statusPublished - 2003

Subject classification (UKÄ)

  • Mathematics


  • geodesic flow
  • diffeomorphism group of the circle


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