Warped product pointwise semi-slant submanifolds of the complex space forms

Abstract

The pointwise semi-slant warped product submanifolds are the natural generalization of the semi-slant, slant, and CR-submanifolds. Recently, Sahin (Port Math, 2013. https://doi.org/10.4171/PM/1934) studied the warped product pointwise semi-slant submanifolds of the Kaehler manifolds and proved the existence of the warped product of the types $N_T\times _\psi N_\theta$ with the warping function $\psi$, where $N_T,$$N_\theta$ are the holomorphic, pointwise slant submanifolds respectively and obtained some basic results. In this paper, the warped product pointwise semi-slant submanifolds of the types $N_T\times _\psi N_\theta$ in the setting of the complex space forms are considered and some characterizing inequalities for the existence of these types of warped products are derived. Moreover, we obtain another inequality for the squared norm of second fundamental form in terms of the warping function and the slant function. This inequality generalizes the inequality that have obtained in Chen (Monatsh Math. 133:177–195, 2001).