Title: Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
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.
Publication Year: 2004
Publication Date: 2004-09-17
Language: en
Type: preprint
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Cited By Count: 4
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