Some characterizing results for hemi-slant warped product submanifolds of a Kaehler manifold

Abstract

Many differential geometric properties of submanifolds of a Kaehler manifold are looked into via canonical structure tensors P and F on the submanifold. For instance, a CR-submanifold of a Kaehler manifold is a CR-product (i.e. locally a Riemannian product of a holomorphic and a totally real submanifold) if and only if the canonical tensor P is parallel on the submanifold. Since, warped product manifolds are generalized version of Riemannian product of manifolds, in this article, we consider the covariant derivatives of the structure tensors on a hemi-slant submanifold of a Kaehler manifold. Our investigations have led us to characterize hemi-slant warped product submanifolds.