Annals of Global Analysis and Geometry

, Volume 44, Issue 4, pp 361–368 | Cite as

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

Article

Abstract

The geodesic distance vanishes on the group \(\text{ Diff }_c(M)\) of compactly supported diffeomorphisms of a Riemannian manifold \(M\) of bounded geometry, for the right invariant weak Riemannian metric which is induced by the Sobolev metric \(H^s\) of order \(0\le s<\tfrac{1}{2}\) on the Lie algebra \(\mathfrak{X }_c(M)\) of vector fields with compact support.

Keywords

Diffeomorphism group Geodesic distance Sobolev metrics of non-integral order 

Mathematics Subject Classification (1991)

Primary 35Q31 58B20 58D05 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Martin Bauer
    • 1
  • Martins Bruveris
    • 2
  • Peter W. Michor
    • 1
  1. 1.Fakultät für MathematikUniversität WienViennaAustria
  2. 2.Institut de mathématiquesEPFLLausanneSwitzerland

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