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Hofer type geometry on the space of Legendrian submanifolds of a contact manifold
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Gheorghe Pitiş
Published/Copyright:
May 15, 2013
Abstract.
The aim of the present paper is to study a Hofer-like geometry on the space of Legendrian submanifolds of a contact manifold. Using contact Hofer energy we define a pseudometric on this space and find sufficient conditions that this be nondegenerate. It is proved that an ample class of distances reduces to multiples of that metric. Examples of subsets with positive contact displacement energy are given.
Keywords: Contact manifold; Lagrangian submanifold; contact fields; Hamiltonian contactomorphisms; Hofer geometry; displacement energy
Received: 2012-10-06
Revised: 2013-03-23
Accepted: 2013-04-01
Published Online: 2013-05-15
Published in Print: 2013-05-01
© 2013 by Walter de Gruyter Berlin Boston
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Keywords for this article
Contact manifold;
Lagrangian submanifold;
contact fields;
Hamiltonian contactomorphisms;
Hofer geometry;
displacement energy
Articles in the same Issue
- Masthead
- Fixed points of asymptotically regular mappings in complex-valued metric spaces
- Coverings of internal groupoids and crossed modules in the category of groups with operations
- A new study on almost increasing and quasi-monotone sequences
- On precompact sets in spaces Cc(X)
- Weighted boundedness for Toeplitz type operators related to Riesz transforms of the Schrödinger operator
- Sums of absolutely nonmeasurable functions
- Symmetry of an integral equation with Bessel potential in ℝn+
- Spanier spaces and the covering theory of non-homotopically path Hausdorff spaces
- On the maximal operator of Marcinkiewicz–Fejér means of the two-dimensional Walsh–Kaczmarz system
- Hofer type geometry on the space of Legendrian submanifolds of a contact manifold
- Initial problems for hyperbolic functional differential systems
- Approximation by complex q-Bernstein–Schurer operators in compact disks
- On some properties of conjugate trigonometric Fourier series
