Volume 15, Issue 2, August 2008, Pages 252 - 269
Decomposition of symmetric tensor fields in the presence of a flat contact pro jective structure
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
Received 12 February 2008, Accepted 14 March 2008, Available Online 1 August 2008.
- https://doi.org/10.2991/jnmp.2008.15.2.10How to use a DOI?
- 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 .
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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 - 1776-0852 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 -