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Poisson Brackets with Prescribed Casimirs

  Published:2011-11-15
 Printed: Oct 2012
  • Pantelis A. Damianou,
    Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
  • Fani Petalidou,
    Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
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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.
Keywords: Poisson bracket, Casimir function, almost symplectic structure, almost cosymplectic structure Poisson bracket, Casimir function, almost symplectic structure, almost cosymplectic structure
MSC Classifications: 53D17, 53D15 show english descriptions Poisson manifolds; Poisson groupoids and algebroids
Almost contact and almost symplectic manifolds
53D17 - Poisson manifolds; Poisson groupoids and algebroids
53D15 - Almost contact and almost symplectic manifolds
 

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