Contact CR-warped product submanifolds in Sasakian manifolds. (English) Zbl 1066.53103

Recently, B.-Y. Chen studied warped products which are CR-submanifolds in Kähler manifolds and established general sharp inequalities for CR-warped products in Kähler manifolds. In the present paper, we obtain 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. The equality case is considered. Also, the minimum codimension of a contact CR-warped product in an odd-dimensional sphere is determined.


53C40 Global submanifolds
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