Geodesic
Nnambu--Poisson structures and their foliations
Lobachevskii journal of mathematics, Tome 3 (1999), pp. 201-207.

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Nambu–Poisson bracket is a natural generalization of Poisson bracket. A very distinguished property is its decomposability. This is investigated from the second order term of the fundamental identity (see [2] or [5]). In this paper, we shall study the first order term of the fundamental identity and get a relation with the Schouten–Nijenhuis bracket. And also we shall show that for a given Poisson structure, the top power of it gives a Nambu–Poisson structure. We shall characterize the Godbillon–Vey class of the foliation defined from a regular Nambu–Poisson tensor.
Mots-clés : Nambu-Poisson structure/bracket/tensor, foliation, Godbillon-Vey class. 
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K. Mikami. Nnambu--Poisson structures and their foliations. Lobachevskii journal of mathematics, Tome 3 (1999), pp. 201-207. http://geodesic.mathdoc.fr/item/LJM_1999_3_a10/