Annals of Global Analysis and Geometry

, Volume 30, Issue 3, pp 299–312

Lengths of Contact Isotopies and Extensions of the Hofer Metric

  • Augustin Banyaga
  • Paul Donato

DOI: 10.1007/s10455-005-9011-7

Cite this article as:
Banyaga, A. & Donato, P. Ann Glob Anal Geom (2006) 30: 299. doi:10.1007/s10455-005-9011-7


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.

Key words

Hofer metricregular contact formCalabi groupCalabi invariantHamiltonian diffeomorphismsstrictly contact diffeomorphismssymplectic diffeomorphisms

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Augustin Banyaga
    • 1
  • Paul Donato
    • 2
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUniversity ParkU.S.A.
  2. 2.L.A.T.P., U.M.R. 6632 Centre de Mathématiques et d'InformatiqueUniversité de ProvenceMarseille (F) Cedex 13France