Compact locally conformally flat Riemannian manifolds

First, we shall prove that a compact connected oriented locally conformally flat n-dimensional Riemannian manifold with constant scalar curvature is isometric to a space form or a Riemannian product Sn-1(c) x S-1 if its Ricci curvature is nonnegative. Second, we shall give a topological classification of compact connected oriented locally conformally flat n-dimensional Riemannian manifolds with nonnegative scalar curvature r if the following inequality is satisfied: Sigma (i,j) R-ij(2) less than or equal to r(2)/(n - 1), where Sigma (i,j) R-ij(2) is the squared norm of the Ricci curvature tensor.