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Recently, B.-Y. Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. Afterwards, I. Hasegawa and the present author obtained a sharp inequality for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Sasakian manifolds. In this paper, we improve the above inequality for contact CR-warped products in Sasakian space forms. Some applications are derived. A classification of contact CR-warped products in spheres, which satisfy the equality case, identically, is given. (2000). 53C40, 53C25. Mathematics Subject Classifications

In this paper, we study the behaviour of submanifolds in statistical manifolds of constant curvature. We investigate curvature properties of such submanifolds. Some inequalities for submanifolds with any codimension and hypersurfaces of statistical manifolds of constant curvature are also established.

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