Abstract
In this paper, we prove that every hemi-slant warped product submanifold of the form
×
in a nearly trans-Sasakian manifold
satisfies the following inequality: ∥
≥
cot
(∥∇̂(ln
)∥
–
), whereas the warped product by reversing these two factors, i.e.,
×
satisfying the inequality:
where
= dim
,
= dim
, ∇̂(ln
) is the gradient of ln
and ∥
∥ is the length of the second fundamental form of the warped product immersion in
. The equality cases of these inequalities are investigated. Furthermore, we discuss some special cases of these inequalities. Finally, we construct two non-trivial examples.