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arXiv · 1211.7254

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

Martin Bauer·Martins Bruveris·Peter W. Michor
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Abstract

The geodesic distance vanishes on the group 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 $0\le s<\tfrac12$ on the Lie algebra $\mathfrak X_c(M)$ of vector fields with compact support.

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Martin Bauer, Martins Bruveris, Peter W. Michor. 2012-11-30. Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II. https://doi.org/10.1007/s10455-013-9370-4

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