Action spectrum and Hofer's distance between Lagrangian submanifolds

Abstract

We give sufficient conditions for geodesics of Hofer's metric in spaces of Hamiltonian deformations of zero section in cotangent bundles over compact smooth manifolds to be minimal. We also prove that the induced distance on the group of Hamiltonian diffeomorphisms gives rise to the distance which is the same as Hofer's distance. © 2002 Elsevier Science B.V. All rights reserved.