On complete spacelike submanifolds with second fundamental form locally timelike in a semi-Riemannian space form

摘要

In this work we obtain a Simon's type inequality for a suitable tensor and apply it in order to obtain some results on a complete n-dimensional spacelike submanifold M-n with parallel mean curvature vector and second fundamental form locally timelike in an (n +p)-dimensional semi-Riemannian space form, N-q(n+p) (c) of index q (1 <= q <= p).