Vanishing Geodesic Distance on Spaces of Submanifolds and Diffeomorphisms
Michor, Peter W.
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CitationMichor, Peter W., and David Bryant Mumford. 2005. Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Documenta Mathematica 10: 217-245.
AbstractThe L^2-metric or Fubini-Study metric on the non-linear
Grassmannian of all submanifolds of type M in a Riemannian manifold (N, g) induces geodesic distance 0. We discuss another metric which involves the mean curvature and shows that its geodesic distance
is a good topological metric. The vanishing phenomenon for
the geodesic distance holds also for all diffeomorphism groups for the
Citable link to this pagehttp://nrs.harvard.edu/urn-3:HUL.InstRepos:3637112
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