The Submanifolds with Parallel Mean Curvature Vector in A Locally Symmetric Riemannian Manifold

Let N n+p be an n+p-dimensional locally symmetric complete Riemannian marifold that its sectional curvature K N Satisfies 12δ≤K N≤1 and M be an n-dimensinal submanifold with parallel mean curvature vector in N n+p .In the paper,we discuss the integral invariant about the square of the norm of the second fundamental form S and the pinching problem of the submanifolds with parallel mean curvature vector in N n+p .