Geometry of Warped Product Semi-Slant Submanifolds of Nearly Kaehler Manifolds.

Non-existence of warped product semi-slant submanifolds of Kaehler manifolds was proved in Sahin (Geom Dedic 117:195-202, 2006), it is interesting to find their existence in a more general setting, e.g., nearly Kaehler manifolds. In this paper, we obtain a necessary and sufficient condition for a semi-slant submanifold of a nearly Kaehler manifold to be a locally warped product. Also, we establish an inequality for the squared norm of the second fundamental form in terms of the warping function and the slant angle. Furthermore, the equality case of the statement is also considered. [ABSTRACT FROM AUTHOR]