Complementary 2-forms of Poisson structures
Izu Vaisman (1996)
Compositio Mathematica
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Izu Vaisman (1996)
Compositio Mathematica
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Rybicki, Tomasz
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Author’s abstract: “We introduce the concept of the flux homomorphism for regular Poisson manifolds. First we establish a one-to-one correspondence between Poisson diffeomorphisms close to and closed foliated 1-forms close to 0. This allows to show that the group of Poisson automorphisms is locally contractible and to define the flux locally. Then, by means of the foliated cohomology, we extend this local homomorphism to a global one”.
Ping Xu (2003)
Annales scientifiques de l'École Normale Supérieure
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Nunes da Costa, J.M. (1997)
Portugaliae Mathematica
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Charles-Michel Marle (2000)
Banach Center Publications
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We obtain conditions under which a submanifold of a Poisson manifold has an induced Poisson structure, which encompass both the Poisson submanifolds of A. Weinstein [21] and the Poisson structures on the phase space of a mechanical system with kinematic constraints of Van der Schaft and Maschke [20]. Generalizations of these results for submanifolds of a Jacobi manifold are briefly sketched.
Ping Xu (1997)
Annales scientifiques de l'École Normale Supérieure
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