Submanifolds With Parallel Mean Curvature Vector In Local Symmetric Spaces

Content: Let Nn+p be an n+p dimensional locally symmetric complete Riemannian manifolds that its sectional KN satisfies 1/2<δ≤KN≤1 and Mn be an ndimensional submanifolds with parallel mean curvature vector in Nn+p.In the paper, we discuss the compact submanifolds and obtains a integral invariant about the square of modulus-length and some theorems about the pinch of the square of modulus-length and the pinch of section curvature . The similar problems in the space of constant curvature are popularzed in the space of local symmetry.