An important thematic into the theory of isometric immersions is the study of geometric properties concerning submanifolds immersed in a semi-Riemannian warped product space of the form \(\epsilon I\times _fM^n\) , where \(M^n\) is an n-dimensional connected oriented Riemannian manifold, \(I\subset \mathbb R\) is an open interval, \(f:I\rightarrow \mathbb R\) is a positive smooth function and \(\epsilon =\pm 1\) , being \(\epsilon =1\) when \(\overline {M}^{n+1}\) is a Riemannian warped product and \(\epsilon = -1\) when \(\overline {M}^{n+1}\) is, according to the terminology established in Alías et al. (Gen. Relat. Grav. 27:71–84, 1995), a generalized Robertson-Walker (GRW) spacetime.