CONTACT CR-WARPED PRODUCT SUBMANIFOLDS OF NEARLY TRANS-SASAKIAN MANIFOLDS

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.