Some linear Jacobi structures on vector bundles

Abstract

We study Jacobi structures on the dual bundle $A^{\ast }$ to a vector bundle $A$ such that the Jacobi bracket of linear functions is again linear and the Jacobi bracket of a linear function and the constant function 1 is a basic function. We prove that a Lie algebroid structure on $A$ and a 1-cocycle $\varphi \in \Gamma (A^{\ast })$ induce a Jacobi structure on $A^{\ast }$ satisfying the above conditions. Moreover, we show that this correspondence is a bijection. Finally, we discuss some examples and applications.

6 pages, To appear in C. R. Acad. Sci. Paris, Série I

References in corpus (1)

• Generalized Lie bialgebroids and Jacobi structures

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