Mathematics – Differential Geometry
Scientific paper
2004-09-17
Documenta Math. 10 (2005), 217--245
Mathematics
Differential Geometry
26 pages, LATEX, final version
Scientific paper
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.
Michor Peter W.
Mumford David
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