Riemannian foliations on manifolds with non-negative curvature (Q1191466)

Any Riemannian foliation \(\mathcal F\) of a complete Riemannian manifold \(M\) (with bundle-like metric) is shown to be totally geodesic provided that the partial Ricci curvature \(R^ L\) of \(M\) (in the direction of \(\mathcal F\)) is non-negative and the norm of the second fundamental form of \(\mathcal F\) is bounded by a constant which depends on codim\(\mathcal F\) and the lower bound for \(R^ L\). Some immediate Corollaries are formulated.