Iglesias, David; Marrero, Juan C. Some linear Jacobi structures on vector bundles. (English. Abridged French version) Zbl 0983.53055 C. R. Acad. Sci., Paris, Sér. I, Math. 331, No. 2, 125-130 (2000). Summary: We study Jacobi structures on the dual bundle \(A^*\) 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 \(\varphi\in\Gamma(A^*)\) induce a Jacobi structure on \(A^*\) satisfying the above conditions. Moreover, we show that this correspondence is a bijection. Finally, we discuss some examples and applications. Cited in 12 Documents MSC: 53D17 Poisson manifolds; Poisson groupoids and algebroids 17B66 Lie algebras of vector fields and related (super) algebras Keywords:Jacobi structures; vector bundle; Jacobi bracket; Lie algebroid PDFBibTeX XMLCite \textit{D. Iglesias} and \textit{J. C. Marrero}, C. R. Acad. Sci., Paris, Sér. I, Math. 331, No. 2, 125--130 (2000; Zbl 0983.53055) Full Text: DOI arXiv