COUPLING POISSON AND JACOBI STRUCTURES ON FOLIATED MANIFOLDS
2004 ◽
Vol 01
(05)
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pp. 607-637
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Keyword(s):
Let M be a differentiable manifold endowed with a foliation ℱ. A Poisson structure P on M is ℱ-coupling if ♯P(ann(Tℱ)) is a normal bundle of the foliation. This notion extends Sternberg's coupling symplectic form of a particle in a Yang–Mills field [11]. In the present paper we extend Vorobiev's theory of coupling Poisson structures [16] from fiber bundles to foliated manifolds 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. We then discuss the extension of the coupling condition to Jacobi structures on foliated manifolds.
2017 ◽
Vol 153
(4)
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pp. 717-744
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1970 ◽
Vol 11
(11)
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pp. 3258-3274
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2008 ◽
Vol 157
(1)
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pp. 1383-1398
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2011 ◽
Vol 44
(31)
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pp. 315401
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1967 ◽
Vol 37
(2)
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pp. 452-464
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