  Motivated by the importance of symplectic isotropic realisations in the study
of Poisson manifolds, this paper investigates the local and global theory of
contact isotropic realisations of Jacobi manifolds, which are those of minimal
dimension. These arise naturally when considering multiplicity-free actions in
contact geometry, as shown in this paper. The main results concern a
classification of these realisations up to a suitable notion of isomorphism, as
well as establishing a relation between the existence of symplectic and contact
isotropic realisations for Poisson manifolds. The main tool is the classical
Spencer operator which is related to Jacobi structures via their associated Lie
algebroid, which allows to generalise previous results as well as providing
more conceptual proofs for existing ones.
