Article (Scientific journals)
Decomposition of symmetric tensor fields in the presence of a flat contact projective structure
Frégier, Yaël; Mathonet, Pierre; Poncin, Norbert
2008In Journal of Nonlinear Mathematical Physics, 15 (2), p. 252-269
Peer Reviewed verified by ORBi
 

Files


Full Text
FreMatPon08.pdf
Publisher postprint (201.33 kB)
Download

All documents in ORBi are protected by a user license.

Send to



Details



Keywords :
Symmetric tensor; Contact Manifold; Projective structure
Abstract :
[en] Let M be an odd-dimensional Euclidean space endowed with a contact 1-form \alpha. 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 \alpha. If we consider symmetric tensor fields with coefficients in tensor densities (also called symbols), the vertical cotangent lift of the contact form \alpha 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 projective contact algebra sp(2n+2) the algebra of vector fields which preserve both the contact structure and the projective 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.
Disciplines :
Mathematics
Author, co-author :
Frégier, Yaël;  University of Luxembourg > Institute of Mathematics
Mathonet, Pierre ;  Université de Liège - ULiège > Département de mathématique > Département de mathématique
Poncin, Norbert;  Univserity of Luxembourg > Institute of Mathematics
Language :
English
Title :
Decomposition of symmetric tensor fields in the presence of a flat contact projective structure
Publication date :
2008
Journal title :
Journal of Nonlinear Mathematical Physics
ISSN :
1402-9251
Publisher :
Atlantis Press, Lulea, Sweden
Volume :
15
Issue :
2
Pages :
252-269
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 20 May 2011

Statistics


Number of views
45 (1 by ULiège)
Number of downloads
177 (2 by ULiège)

Scopus citations®
 
1
Scopus citations®
without self-citations
1
OpenCitations
 
1

Bibliography


Similar publications



Contact ORBi