Embeddings of compact Sasakian manifolds

Let M be a compact Sasakian manifold. We show that M admits a CR-embedding into a Sasakian manifold diffeomorphic to a sphere, and this embedding is compatible with the respective Reeb fields. We argue that a stronger embedding theorem cannot be obtained. We use an extension theorem for Kahler geometry: given a compact Kahler manifolds X subset of Y, and a Kahier form omega(X) on X which lies in a Kahler class [omega] of Y restricted to X, wX can be extended to a Kahler form omega y on Y.