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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dc.contributor.author Michor, Peter W.
dc.contributor.author Mumford, David Bryant
dc.date.accessioned 2010-02-12T19:38:51Z
dc.date.issued 2005
dc.identifier.citation Michor, Peter W., and David Bryant Mumford. 2005. Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Documenta Mathematica 10: 217-245. en_US
dc.identifier.issn 1431-0643 en_US
dc.identifier.issn 1431-0635 en_US
dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:3637112
dc.description.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. en_US
dc.description.sponsorship Mathematics en_US
dc.language.iso en_US en_US
dc.publisher Universität Bielefeld, Fakultät für Mathematik en_US
dc.relation.isversionof http://www.math.uiuc.edu/documenta/ en_US
dc.relation.hasversion http://www.dam.brown.edu/people/mumford/Papers/DigitizedVisionPapers--forNonCommercialUse/x05b--Vanishing-Michor.pdf en_US
dash.license LAA
dc.title Vanishing Geodesic Distance on Spaces of Submanifolds and Diffeomorphisms en_US
dc.type Journal Article en_US
dc.description.version Version of Record en_US
dc.relation.journal Documenta Mathematica en_US
dash.depositing.author Mumford, David Bryant
dc.date.available 2010-02-12T19:38:51Z

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  • FAS Scholarly Articles [7362]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University

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