Decomposition of foliations and ruled submanifolds of nonnegative mixed curvature (Q1916555)

The decompositions of foliations and ruled submanifolds are considered. The paper contains a new synthetic method based on the Ferus condition and the matrix Riccati equation. Let \(\{L\}\) be a compact totally geodesic foliation of the Riemannian manifold \(M\). The paper gives the conditions for \(M\) to be locally isometric to the product \(L \times L^\perp\).