  Compared to totally umbilical submanifolds, studies on pseudo-umbilical
submanifolds are quite limited. In this paper, pseudo-umbilical submanifolds of
locally product Riemannian manifolds are studied. Necessary and sufficient
conditions for a pseudo umbilical submanifold to be invariant, or
anti-invariant or semi-invariant submanifold are obtained by using projections
arisen from the product structure of a locally product Riemannian manifold.
