Locally conformally flat manifolds with constant scalar curvature

Abstract

Let ( M n , g ) (M^n,g) be an n n -dimensional ( n ≥ 4 ) (n\geq 4) compact locally conformally flat Riemannian manifold with constant scalar curvature and constant squared norm of Ricci curvature. Applying the moving frame method, we prove that such a Riemannian manifold does not exist if its Ricci curvature tensor has three distinct eigenvalues.