Journal of Nonlinear Mathematical Physics

Volume 15, Issue 2, August 2008, Pages 252 - 269

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

Authors
Yael FREGIER 0, Pierre MATHONET 1, Norbert PONCIN 2
0University of Luxembourg, Campus Limpertsberg, Institute of Mathematics
1University of Liege, Department of mathematics
2University of Luxembourg, Campus Limpertsberg, Institute of Mathematics
Available Online 19 August 2008.
DOI
https://doi.org/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].
Open Access
This is an open access article distributed under the CC BY-NC license.

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
15 - 2
Pages
252 - 269
Publication Date
2008/08
ISSN
1402-9251
DOI
https://doi.org/10.2991/jnmp.2008.15.2.10How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Yael FREGIER
AU  - Pierre MATHONET
AU  - Norbert PONCIN
PY  - 2008
DA  - 2008/08
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  - 1402-9251
UR  - https://doi.org/10.2991/jnmp.2008.15.2.10
DO  - https://doi.org/10.2991/jnmp.2008.15.2.10
ID  - FREGIER2008
ER  -