Kentaro Mikami

Nambu-Poisson structures and their foliations

(Lobachevskii Journal of Mathematics, Volume III)

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 [Gauth:LMP] or [nakanisi:nambu]). 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.
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