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 i sometric 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 classificati on of compact connected oriented locally conformally flat n-dimensional Rie mannian manifolds with nonnegative scalar curvature r if the following ineq uality 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 tens or.