Riemannian foliations admitting transversal conformal fields

Let ( M, gM, F) be a closed, connected Riemannian manifold with a foliation F of codimension q and a bundle-like metric g(M). We study the relationship between several infinitesimal automorphisms. Moreover under the some curvature condition, if M admits a transversal conformal field, then F is transversally isometric to the action of a finite subgroup of O(q) acting on the q-sphere of constant curvature.