Geodesic
Poisson Brackets with Prescribed Casimirs
Canadian journal of mathematics, Tome 64 (2012) no. 5, pp. 991-1018

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DOI

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 using a convenient almost cosymplectic structure. Several examples and applications are presented.
DOI : 10.4153/CJM-2011-082-2
Mots-clés : 53D17, 53D15, Poisson bracket, Casimir function, almost symplectic structure, almost cosymplectic structure 
Damianou, Pantelis A.; Petalidou, Fani. Poisson Brackets with Prescribed Casimirs. Canadian journal of mathematics, Tome 64 (2012) no. 5, pp. 991-1018. doi: 10.4153/CJM-2011-082-2
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     title = {Poisson {Brackets} with {Prescribed} {Casimirs}},
     journal = {Canadian journal of mathematics},
     pages = {991--1018},
     year = {2012},
     volume = {64},
     number = {5},
     doi = {10.4153/CJM-2011-082-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2011-082-2/}
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