Abstract
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.
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Mathematics Subject Classifications (2000). 53C40, 53C25.
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Mihai, I. Contact CR-Warped Product Submanifolds in Sasakian Space Forms . Geom Dedicata 109, 165–173 (2004). https://doi.org/10.1007/s10711-004-5459-z
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DOI: https://doi.org/10.1007/s10711-004-5459-z