The paper presents a simple proof of a theorem by Q-M. Cheng  on compact locally conformally flat Riemannian manifolds and  shows that a complete connected oriented hypersurface in  $S^{n+1}$ with nonnegative Weyl tensor and Ricci curvature is  isometric to a space form or a Riemannian product $S^{n-1}\times S^1$.