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Some linear Jacobi structures on vector bundles

David Iglesias·Juan C. Marrero
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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 $ϕ\in Γ(A^\ast)$ 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.

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David Iglesias, Juan C. Marrero. 2000-07-24. Some linear Jacobi structures on vector bundles. https://doi.org/10.1016/s0764-4442(00)00512-7

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