Geometry of Warped Product Pointwise Semi-Slant Submanifolds of Kaehler Manifolds

Abstract

In the present paper, we prove some potential results for the existence of warped product pointwise semi-slant submanifolds of Kaehler manifolds by it characterization in terms of tensor fields. Moreover, firt of all we consider the non-trivial warped product such that the spherical submanifold is pointwise slant. Next we obtain some geometric and topological properties to derive an inequality for the second fundamental forms of warped product pointwise semi-slant submanifold in Kaehler manifold. Further, we give some applications on such inequalities in complex space forms. After that, we construct the necessary and sufficient conditions for the non-existence of compact warped product pointwise semi-slant submanifold in complex space forms and the equality cases are also considered.