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

Abstract

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 ).