Vanishing Geodesic Distance on Spaces of Submanifolds and Diffeomorphisms

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Vanishing Geodesic Distance on Spaces of Submanifolds and Diffeomorphisms

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Title: Vanishing Geodesic Distance on Spaces of Submanifolds and Diffeomorphisms
Author: Michor, Peter W.; Mumford, David Bryant

Note: Order does not necessarily reflect citation order of authors.

Citation: Michor, Peter W., and David Bryant Mumford. 2005. Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Documenta Mathematica 10: 217-245.
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Abstract: The 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 L^2-metric.
Published Version: http://www.math.uiuc.edu/documenta/
Other Sources: http://www.dam.brown.edu/people/mumford/Papers/DigitizedVisionPapers--forNonCommercialUse/x05b--Vanishing-Michor.pdf
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:3637112

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  • FAS Scholarly Articles [6948]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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