Spacelike submanifolds with parallel mean curvature vector in S n+p q (1)

Let M n be a complete spacelike submanifold in an indefinite space form S + (1). When p = q, there are numerous rigidity results concerning submanifolds with parallel mean curvature vector. However, there are few results concerning the case q < p. In this paper, we will focus on this kind of submanifold and give some classifications of submanifolds with parallel mean curvature vector according to the squared norm of the second fundamental form.