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Poisson brackets with prescribed Casimirs

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      Abstract

      We consider the problem of constructing Poisson brackets on smooth manifolds \(M\) with prescribed Casimir functions. If \(M\) is of even dimension, we achieve our construction by considering a suitable almost symplectic structure on \(M\), while, in the case where \(M\) is of odd dimension, our objective is achieved by using a convenient almost cosymplectic structure. Several examples and applications are presented.

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      Most cited references 12

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      The local structure of Poisson manifolds

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            Author and article information

            Journal
            04 March 2011
            1103.0849

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

            Custom metadata
            53D17, 53D15
            24 pages
            math.DG

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