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Annals of Global Analysis and Geometry

, Volume 28, Issue 3, pp 301–308 | Cite as

Averaging of Legendrian Submanifolds of Contact Manifolds

  • Marco ZambonEmail author
Article
  • 47 Downloads

Abstract

We give a procedure to ‘average’ canonically C1-close Legendrian submanifolds of contact manifolds. As a corollary we obtain that, whenever a compact group action leaves a Legendrian submanifold almost invariant, there is an invariant Legendrian submanifold nearby.

Keywords

contact manifold invariant submanifold Legendrian submanifold 

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References

  1. 1.
    Cannas da Silva, A.: Lectures on Symplectic Geometry, Lecture Notes in Math 1764, Springer, Berlin, 2000.Google Scholar
  2. 2.
    Weinstein, A.: Almost invariant submanifolds for compact group actions, J. Eur. Math. Soc. 2 (1999), 53–86.CrossRefGoogle Scholar
  3. 3.
    Zambon, M.: Submanifold averaging in riemannian and symplectic geometry. Preprint ArXiv.DG/0208203, to appear in J. Eur. Math. Soc.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsUC BerkeleyU.S.A.

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