Hofer’s metric is a metric on the group of Hamiltonian diffeomorphisms of a symplectic manifold. This group is infinite-dimensional, so that the existence of this metric is a very nontrivial due noncompactness. The subject of Hofer’s geometry is now a classic subject in symplectic geometry.

References

Helmut Hofer, The topology of symplectic maps, Proceedings of the Royal Society of Edinburgh, 115 (1990), 25-38.

Lev Buhovsky, Yaron Ostrover, On the uniqueness of Hofer’s geometry, arxiv:1008.0661

Michael Usher, Hofer geometry and cotangent fibers, arxiv/1301.4484

Revised on January 21, 2013 17:20:01
by Zoran Škoda
(161.53.130.104)