Journal of the
Korean Mathematical Society JKMS

Recently, Chen studied warped products which are $CR$-submanifolds in Kaehler manifolds and established general sharp inequalities for $CR$-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates 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 Kenmotsu space forms. The equality case is considered. Some applications are derived.

Keywords: contact $CR$-submanifold, warped product, Kenmotsu manifold, Kenmotsu space form

MSC numbers: 53C40, 53C25, 54D10