Reduction of Jacobi manifolds via Dirac structures theory

Details Reduction of Jacobi manifolds via Dirac structures theory Reduction of Jacobi manifolds via Dirac structures theory

2004-12-11

arxiv.org/abs/math/0412221v1

Mathematics

Symplectic Geometry

18 pages

Scientific paper

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 $(M,\Lambda,E)$ 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.

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