  In this paper we show explicit examples of several families of immersions
with constant mean curvature and non constant principal curvatures, in
semi-riemannian manifolds with constant sectional curvature. In particular, we
prove that every h in [-1,-2 sqrt{n-1}/n) can be realized as the constant
curvature of a complete immersion of S_1^{n-1} x R in the (n+1)-dimensional de
Sitter space S_1^{n+1}. We provide 3 types of immersions with cmc in the
Minkowski space, 5 types of immersion with cmc in the de Sitter space and 5
types of immersion with cmc in the anti de Sitter space. At the end of the
paper we analyze the families of examples that can be extended to closed
hypersurfaces.
