A general inequality for pointwise semi-slant warped products in nearly Kenmotsu manifolds


Siraj Uddin, Ashwaq Altalhi, Nadia Alluhaibi




In this paper, we prove that every pointwise semi-slant warped product submanifold M = NT× f Nθ in a nearly Kenmotsu manifold M˜ satisfies the following inequality: ‖h‖2 ≥ 2n2 ( 1 + 109 cot 2 θ ) ( ‖∇ˆ(ln f )‖2 − 1 ) , where n2 = dim Nθ, ∇ˆ(ln f ) is the gradient of ln f and ‖h‖ is the length of the second fundamental form of M. The equality and special cases of the inequality are investigated