Conformal Rigidity Of Einstein Manifolds

In this paper,we show that a compact Riemannian manifold with constant scalar curvature can be c.onformally deformed to a Einstein manifold and we prove the following conclusion:1.Einstein manifolds with non-positive scalar curvature cannot conformally deform to another Einstein manifold,that is to say,they are rigid.2.The necessary condition for a Riemannian manifold with positive scalar curvature can conformally deform to an Einstein manifold is max||Ric-R/ng||2?cnc(?1-c),where cn =(n-2)2/b,c=R/n-1,?1 is first eigenvalue of the Laplace operator for the mea-sure g.The equality sign holds if and only if(Mn,g)is isometric with a sphere Sn(r)(r =1/(?)).