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 $\|h\|^2\geq 2s[\|\nabla lnf\|^2+\alpha ^2 -\beta^2]$, for contact CR-warped products of nearly trans-Sasakian manifolds. Our inequality generalizes all derived inequalities for contact CR-warped products either in any contact metric manifold. The equality case is also handled.
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