Vanishing Geodesic Distance on Spaces of Submanifolds and Diffeomorphisms
نویسندگان
چکیده
The L-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-metric.
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ar X iv : m at h . D G / 0 40 93 03 v 1 1 7 Se p 20 04 VANISHING GEODESIC DISTANCE ON SPACES OF SUBMANIFOLDS AND DIFFEOMORPHISMS
The L-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-metric.
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