Characterizations of pseudo-umbilical submanifolds of locally product Riemannian manifolds

Abstract

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.