Poly-Poisson structures
Differential Geometry
2012-09-19 v1 Mathematical Physics
math.MP
Symplectic Geometry
Abstract
In this paper we introduce poly-Poisson structures as a higher-order extension of Poisson structures. It is shown that any poly-Poisson structure is endowed with a polysymplectic foliation. It is also proved that if a Lie group acts polysymplectically on a polysymplectic manifold then, under certain regularity conditions, the reduced space is a poly-Poisson manifold. In addition, some interesting examples of poly-Poisson manifolds are discussed.
Cite
@article{arxiv.1209.4003,
title = {Poly-Poisson structures},
author = {D. Iglesias-Ponte and J. C. Marrero and M. Vaquero},
journal= {arXiv preprint arXiv:1209.4003},
year = {2012}
}
Comments
23 pages