In this paper we study some compact locally conformally flat manifolds with a compatible metric whose scalar curvature is nonnegative, and in particular with nonnegative Ricci curvature, In the last section we study such manifolds of dimension 4 and scalar curvature identically zero.
Abstract.It is shown that any complete, noncompact, simply connected Riemannian manifold with nonnegative curvature operator is isometric to the product of its compact soul (in the sense of Cheeger-Gromoll) and a complete manifold diffeomorphic to a Euclidean space
In this paper we study compact manifolds with 2-nonnegative Ricci operator, assuming that their Weyl operator satisfies certain conditions which generalize conformal flatness. As a consequence, we obtain that such manifolds are either locally symmetric or their Betti numbers between 2 and n − 2 vanish. We also study the topology of compact hypersurfaces with 2-nonnegative Ricci operator.
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