On Submanifolds in Locally Symmetric and Conformally Flat Riemannian Manifolds

Let N n+p be an (n+p)-dimensional locally symmetric and conformally flat Riemannian manifold and Mn be an n-dimensional compact submanifold minimally immersed in N n+p. Instead of (n+p)-dimensional unit sphere, we generalize Pinching Theorems about submanifolds in unit sphere and get theorems about submanifolds in locally symmetric and conformally flat Riemannian manifold.