Geodesics of Hofer's metric on the space of Lagrangian submanifolds

Details Geodesics of Hofer's metric on the space of Lagrangian submanifolds Geodesics of Hofer's metric on the space of Lagrangian submanifolds

2006-08-03

arxiv.org/abs/math/0608082v1

Mathematics

Symplectic Geometry

14 pages

Scientific paper

We study geodesics of Hofer's metric on the space of Lagrangian submanifolds
in arbitrary symplectic manifolds from the variational point of view. We give a
characterization of length-critical paths with respect to this metric. As a
result, we prove that if two Lagrangian submanifolds are disjoint then we
cannot join them by length-minimizing geodesics.

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