Abstract
Recently, many authors studied the relations between the squared norm of the second fundamental form (extrinsic invariant) and the warping function (intrinsic invariant) for warped product submanifolds (see [1, 7, 14]). Inspired by those relations we establish a general sharp inequality, namely parallel to h parallel to(2) >= 2s[parallel to del lnf parallel to(2) + alpha(2) - beta(2)], for contact CR-warped products of nearly trans-Sasakian manifolds. Our inequality generalizes all derived inequalities for contact CRwarped products either in any contact metric manifold. The equality case is also handled.