Warped Product Submanifolds of Kenmotsu Manifolds with Slant Fiber

Monia Fouad Naghi, Siraj Uddin, Falleh R Al-Solamy

Recently, we have discussed the warped product pseudo-slant submanifolds of the type M θ × f M ⊥ of Kenmotsu manifolds. In this paper, we study other type of warped product pseudo-slant submanifolds by reversing these two factors in Kenmotsu manifolds. The existence of such warped product immersions is proved by a characterization. Also, we provide an example of warped product pseudo-slant submanifolds. Finally, we establish a sharp estimation such as h 2 ≥ 2p cos 2 θ ∇(ln f) 2 − 1 for the squared norm of the second fundamental form h 2 , in terms of the warping function f , where ∇(ln f) is the gradient vector of the function ln f. The equality case is also discussed.