Totally umbilical submanifolds in pseudo-Riemannian space forms

A totally umbilical submanifold in pseudo-Riemannian manifolds is a fundamental notion, which characterized by the condition that second form proportional to metric. It also generalization of notion geodesic submanifold. In this paper, we classify congruent classes full submanifolds non-flat space forms, and consider their moduli spaces. As consequence, show some spaces isometric immersions between forms one same constant curvature are non-Hausdorff.