Warped product submanifolds of Kaehler manifolds with a slant factor.
(Warped product submanifolds of Kähler manifolds with a slant factor.)

*(English)*Zbl 1162.53040Summary: Recently, we showed that there exist no warped product semi-slant submanifolds in Kähler manifolds. On the other hand, Carriazo introduced anti-slant submanifolds as a particular class of bi-slant submanifolds. In this paper, we study such submanifolds in detail and show that they are useful to define a new kind of warped product submanifolds of Kähler manifolds. In this direction, we obtain the existence of warped product hemi-slant (anti-slant) submanifolds with examples. We give a characterization theorem and establish an inequality for the squared norm of the second fundamental form in terms of the warping function for such submanifolds. The equality case is also considered.