Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
Peter W. MichorFakultät für Mathematik Division of Applied Mathematics Universität Wien Brown University Nordbergstrasse 15 Box F, Providence, RI 02912, USA A-1090 Wien, Austria David
David Mumfordand Erwin Schrödinger Institut für Mathematische Physik Boltzmanngasse 9 A-1090 Wien, Austria
The -metric or Fubini-Study metric on the non-linear Grassmannian of all submanifolds of type in a Riemannian manifold 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 -metric.
Cite this article
Peter W. Michor, David Mumford, Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Doc. Math. 10 (2005), pp. 217–245DOI 10.4171/DM/187