Lengths of Contact Isotopies and Extensions of the Hofer Metric |
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| Authors: | Augustin Banyaga Paul Donato |
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| Institution: | (1) Department of Mathematics, The Pennsylvania State University, University Park, PA, 16802, U.S.A.;(2) L.A.T.P., U.M.R. 6632 Centre de Mathématiques et d'Informatique, Université de Provence, 39, rue F. Joliot Curie, 13453 Marseille (F) Cedex 13, France |
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| Abstract: | Using the Hofer metric, we construct, under a certain condition, a bi-invariant distance on the identity component in the group of strictly contact diffeomorphisms of a compact regular contact manifold. We also show that the Hofer metric on Ham(M) has a right-invariant (but not left invariant) extension to the identity component in the groups of symplectic diffeomorphisms of certain symplectic manifolds.Mathematics Subject classification (2000): 53C12, 53C15. |
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| Keywords: | Hofer metric regular contact form Calabi group Calabi invariant Hamiltonian diffeomorphisms strictly contact diffeomorphisms symplectic diffeomorphisms |
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