Bigébroïdes de quasi-Jacobi exacts

Quasi-Jacobi bialgebroids are natural generalizations, introduced by Nunes da Costa and Petalidou, of both Jacobi bialgebroids and quasi-Lie bialgebroids. For a given vector bundle \(A \rightarrow M\) and a Jacobi algebroid structure on dual vector bundle \(A^* \rightarrow M\), we show that we can construct the particular quasi-Jacobi bialgebroid structures, by the choice of a section of \(\Lambda ^2 A^*\). We define a relation of equivalence on new structures and we show that there is a correspondance 1-to-1 between the Jacobi algebroid structures on dual vector bundle and equivalence classes of constructed structures.