On Submanifolds in Locally Symmetric and Conformally Flat Riemannian Manifolds

Let Nn p be an (n p )-dimensional locally symmetric and conformally flat Riemannian manifold and Mn be an n-dimensional compact submanifold minimally immersed in Nn 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.