On Submanifolds in Locally Symmetric and Conformally Flat Riemannian Manifolds

摘要

Let N~(n+p) be an (n + p) -dimensional locally symmetric and conformally flat Riemannian manifold and M~n 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.