Decomposition of symmetric tensor fields in the presence of a flat contact pro jective structure

DOI

10.2991/jnmp.2008.15.2.10How to use a DOI?

Abstract

Let M be an odd-dimensional Euclidean space endowed with a contact 1-form ?. We investigate the space of symmetric contravariant tensor fields over M as a module over the Lie algebra of contact vector fields, i.e. over the Lie subalgebra made up of those vector fields that preserve the contact structure defined by ?. If we consider symmetric tensor fields with coefficients in tensor densities (also called symbols), the vertical cotangent lift of the contact form ? defines a contact invariant operator. We also extend the classical contact Hamiltonian to the space of symbols. This generalized Hamiltonian operator on the space of symbols is invariant with respect to the action of the pro jective contact algebra sp(2n + 2) the algebra of vector fields which preserve both the contact structure and the pro jective structure of the Euclidean space. These two operators lead to a decomposition of the space of symbols, except for some critical density weights, which generalizes a splitting proposed by V. Ovsienko in [18].

Copyright

© 2008, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Yaël Fregier
AU  - Pierre Mathonet
AU  - Norbert Poncin
PY  - 2008
DA  - 2008/08/01
TI  - Decomposition of symmetric tensor fields in the presence of a flat contact pro jective structure
JO  - Journal of Nonlinear Mathematical Physics
SP  - 252
EP  - 269
VL  - 15
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2008.15.2.10
DO  - 10.2991/jnmp.2008.15.2.10
ID  - Fregier2008
ER  -