Pointwise hemi-slant warped product submanifolds in nearly Kaehler manifolds

In this paper, we introduce the notion of pointwise hemi-slant sub-manifolds of nearly Kaehler manifolds. Further, we study their warped products and prove the necessary and sufficient condition that a point-wise hemi-slant submanifold to be a warped product manifold. Also, we establish a sharp inequality for the pointwise hemi-slant warped product submanifolds of the form M = M_⊥ ×_f M_θ which is mixed totally geodesic in an arbitrary nearly Kaehler manifold ~M. The equality case is also discussed.