Totally umbilical, pseudo-umbilical and pointwise slant submanifolds in Kaehler manifolds

Abstract

In this paper, pointwise slant submanifolds of a Kaehler manifold are studied. First of all, if the submanifold of a Kaehler manifold is totally umbilical or pseudo-umbilical, the conditions for this submanifold to be a pointwise slant are investigated. Then given a pointwise submanifold of a Kaehler manifold, we investigate the conditions for this submanifold to be holomorphic, totally real, slant or CR-submanifold and obtain conditions depending on the behavior of the projections defined on the submanifold and the sectional curvature. Certain conditions are also found for the submanifold to be totally geodesic.