12 research outputs found
Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
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.Comment: 26 pages, LATEX, final versio