Reduction of Jacobi manifolds via Dirac structures theory

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Abstract

We first recall some basic definitions and facts about Jacobi manifolds, generalized Lie bialgebroids, generalized Courant algebroids and Dirac structures. We establish an one-one correspondence between reducible Dirac structures of the generalized Lie bialgebroid of a Jacobi manifold (M, Λ, E) for which 1 is an admissible function and Jacobi quotient manifolds of M. We study Jacobi reductions from the point of view of Dirac structures theory and we present some examples and applications. © 2005 Elsevier B.V. All rights reserved.

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Petalidou, F., & Nunes da Costa, J. M. (2005). Reduction of Jacobi manifolds via Dirac structures theory. Differential Geometry and Its Application, 23(3), 282–304. https://doi.org/10.1016/j.difgeo.2005.06.003

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