On the geometric quantization of Jacobi manifolds

29 pages.The geometric quantization of Jacobi manifolds is discussed. A natural cohomology (termed Lichnerowicz–Jacobi) on a Jacobi manifold is introduced, and using it the existence of prequantization bundles is characterized. To do this, a notion of contravariant derivatives is used, in such a way that the procedure developed by Vaisman for Poisson manifolds is naturally extended. A notion of polarization is discussed and the quantization problem is studied. The existence of prequantization representations is also considered.This work has been partially supported through grants DGICYT (Spain) (Project No. PB94- 0106) and University of La Laguna (Spain).Peer reviewe