Topology of codimension-one foliations of nonnegative curvature

We show that a transversely oriented $C^2$-foliation of codimension one with nonnegative Ricci curvature on a closed orientable manifold is a foliation with almost no holonomy. This allows us to decompose the manifold into blocks on which this foliation has a simple structure. We also show that a manifold homeomorphic to a 5-dimensional sphere does not admit a codimension-one $C^2$-foliation with nonnegative sectional curvature.
Bibliography: 29 titles.