Jacobi structures on affine bundles (Q2641542)

This paper studies Jacobi structures on affine bundles. It is well-known that linear Poisson structures are in one-to-one correspondence with the Lie algebroid structures on the dual vector bundle. The author proves the bijective correspondence between affine Jacobi structures and Lie algebroid structures. The passage from Poisson structures and Lie algebroid structures to Jacobi structures is in fact the passage from derivation to first-order differential operators. Examples and applications of this correspondence are finally given.