Pinching theorems for compact spacelike submanifolds in semi-Riemannian space forms

Let Mn be a compact spacelike submanifold of a semi-Riemannian manifold Mpn+p(c) of constant curvature c, whose index is p, with nonzero mean curvature H and parallel mean curvature vector. We prove that there exists a positive constant C=C(n,H) such that if ‖S‖n2