Mathematics – Symplectic Geometry
Scientific paper
2004-02-23
Mathematics
Symplectic Geometry
LateX, 38 pages
Scientific paper
Let M be a differentiable manifold endowed with a foliation F. A Poisson structure P on M is F-coupling if the image of the annihilator of TF by the sharp-morphism defined by P is a normal bundle of the foliation F. This notion extends Sternberg's coupling symplectic form of a particle in a Yang-Mills field. In the present paper we extend Vorobiev's theory of coupling Poisson structures from fiber bundles to foliations and give simpler proofs of Vorobiev's existence and equivalence theorems of coupling Poisson structures on duals of kernels of transitive Lie algebroids over symplectic manifolds. Then we discuss the extension of the coupling condition to Jacobi structures on foliated manifolds.
No associations
LandOfFree
Coupling Poisson and Jacobi structures on foliated manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Coupling Poisson and Jacobi structures on foliated manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Coupling Poisson and Jacobi structures on foliated manifolds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-349724