A GENERALIZATION OF THE BOOTHBY-WANG THEOREM

We consider a Riemannian manifold M with an f-structure. With some additional properties such a manifold is called a K, C or J-manifold. The considered structures determine a Riemannian foliation, whose leaf closures form a singular Riemannian foliation. We give conditions under which the foliation of the principal stratum is again associated to a structure of the type we consider. The manifold can be partitioned into strata on which the leaf closures are given by toroidal fiber bundles. This theorem is a topological generalization of the classical Boothby-Wang theorem for the contact manifolds.