Vanishing Geodesic Distance on Spaces of Submanifolds and Diffeomorphisms

Vanishing Geodesic Distance on Spaces of Submanifolds and Diffeomorphisms

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Vanishing Geodesic Distance on Spaces of Submanifolds and Diffeomorphisms

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