Complementary 2-forms of Poisson structures

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Let (M, P) be a Poisson manifold. A 2-form ω of M such that the Koszul bracket {ω,ω} P = 0 is called a complementary form of P. Every complementary form yields a new Lie algebroid structure of TM, and, under some supplementary hypothesis, the form also defines a Poisson-Nijenhuis structure of M [12]. We give several examples of complementary forms, and new examples of Poisson-Nijenhuis manifolds. The general results are expressed in the framework of Hamiltonian structures [3] and Lie algebroids.

Original languageEnglish
Pages (from-to)55-75
Number of pages21
JournalCompositio Mathematica
Issue number1
StatePublished - 1996

ASJC Scopus subject areas

  • Algebra and Number Theory


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