Research On Several Problems Of Einstein Manifold

This paper deales with Einstein manifold and Einstein submanifold in the space with constant sectional curvature,obtain some properties about Einstein manifold and a few pinching theorems of this kind of Riemann manifold.As the following:1. (M,g)is Einstein Manifold,dimM=n\4,then there are12(n-1)(n-2)sections in(M,g),the sum of the sesectional curvatures is constant.2. Riemann manifold(M~n,g)(n\5)with parallel ricci curvature is not Einstein manifold,M_t is Einstein subspaceof(M~n,g)and dim M_t\4,then3. Misa compact Einstein hypersurface in S~4 with constant mean curvature ifthenR=0...