Some complete manifolds with non-negative curvature operator. (English) Zbl 0602.53033
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.
Keywords:
complete non-compact manifold; curvature operator; soul; sectional curvatures; flat normal bundleReferences:
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