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.
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Martin Bauer was supported by ‘Fonds zur Förderung der wissenschaftlichen Forschung, Projekt P 24625’.
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Bauer, M., Bruveris, M. & Michor, P.W. Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II. Ann Glob Anal Geom 44, 361–368 (2013). https://doi.org/10.1007/s10455-013-9370-4
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DOI: https://doi.org/10.1007/s10455-013-9370-4