Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms
Peter Michor
(University of Vienna)
Abstract:
The L2-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 L2-metric. A special case
is Burgers' equation.