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.
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Mathematics Subject classification (2000): 53C12, 53C15.
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Banyaga, A., Donato, P. Lengths of Contact Isotopies and Extensions of the Hofer Metric. Ann Glob Anal Geom 30, 299–312 (2006). https://doi.org/10.1007/s10455-005-9011-7
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DOI: https://doi.org/10.1007/s10455-005-9011-7