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Integrability of Jacobi and Poisson structures

Marius Crainic, Chenchang Zhu (2007)

Annales de l’institut Fourier

We discuss the integrability of Jacobi manifolds by contact groupoids, and then look at what the Jacobi point of view brings new into Poisson geometry. In particular, using contact groupoids, we prove a Kostant-type theorem on the prequantization of symplectic groupoids, which answers a question posed by Weinstein and Xu. The methods used are those of Crainic-Fernandes on A -paths and monodromy group(oid)s of algebroids. In particular, most of the results we obtain are valid also in the non-integrable...

Integrability of the Poisson algebra on a locally conformal symplectic manifold

Haller, Stefan, Rybicki, Tomasz (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

Summary: It is proven that the Poisson algebra of a locally conformal symplectic manifold is integrable by making use of a convenient setting in global analysis. It is also observed that, contrary to the symplectic case, a unified approach to the compact and non-compact case is possible.

Integrable hierarchies and the modular class

Pantelis A. Damianou, Rui Loja Fernandes (2008)

Annales de l’institut Fourier

It is well-known that the Poisson-Nijenhuis manifolds, introduced by Kosmann-Schwarzbach and Magri form the appropriate setting for studying many classical integrable hierarchies. In order to define the hierarchy, one usually specifies in addition to the Poisson-Nijenhuis manifold a bi-hamiltonian vector field. In this paper we show that to every Poisson-Nijenhuis manifold one can associate a canonical vector field (no extra choices are involved!) which under an appropriate assumption defines an...

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