Parallel Codazzi tensors with submanifold applications

Abstract A decomposition theorem is established for a class of closed Riemannian submanifolds immersed in space form the constant sectional curvature. In particular, it shown that if M has nonnegative curvature and admits Codazzi tensor with “parallel mean curvature”, then locally isometric to direct product irreducible factors determined by spectrum tensor. This global when simply connected, generalizes what known parallel vector.