Warped product submanifolds of Kenmotsu manifolds with slant fiber

Monia Naghi, Siraj Uddin, Falleh Al-Solamy
2018 Filomat  
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
more » ... ) 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.
doi:10.2298/fil1806115n fatcat:clmwqgpypnd4fdmaxqnigey4rm