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Coupling Poisson and Jacobi structures on foliated manifolds. (English) Zbl 1079.53130

From the summary: We extend Yu. M. Vorob’ev’s theory of coupling Poisson structures [ Lie algebroids and related topics in differential geometry (Warsaw, 2000), Banach Cent. Publ. 54, 249–274 (2001; Zbl 1007.53062)] 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.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)

Citations:

Zbl 1007.53062
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References:

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