Some complete manifolds with non-negative curvature operator (Q1081846)

We study the topology of a complete non-compact manifold \(M^ n\). We prove that if \(\pi _ l(M)=\{0\}\) and the curvature operator\(\rho\) is non-negative then M is a topological product of a soul by a Euclidean space. We apply this result in two cases when the non-negativity of the sectional curvatures (k\(\geq 0)\) implies the non-negativity of \(\rho\). We also obtain similar conclusion when M is isometrically immersed in Euclidean space with codimension two and flat normal bundle.