This paper investigates compact spacelike submanifolds \(M^n\) immersed in a pseudo-Riemannian space form \(N_{p}^{n+p}(c)\) , in particular in the pseudo-Euclidean space \({\mathbb {R}}_{p}^{n+p}\) and the de Sitter space \(M_{p}^{n+p}(c)\) , assuming the flatness of the normal bundle. Under some intrinsic conditions on \(M^n\) , we give a classification in \(N_{p}^{n+p}(c)\) . We also present examples of submanifolds, sustaining the statements of the theorems.
