Abstract
We call a submanifold M of a Kaehler manifold (M) over tilde a pointwise CR-slant warped product if it is a warped product, B x(f) N-theta, of a CR-product B = N-T x N-perpendicular to and a proper pointwise slant submanifold N-theta with slant function theta, where N-T and N-perpendicular to are complex and totally real submanifolds of (M) over tilde. We prove that if a pointwise CR-slant warped product B x(f) N-theta with B = N-T x N-perpendicular to in a Kaehler manifold is weakly D-theta-totally geodesic, then it satisfies
parallel to sigma parallel to(2) >= 4s {(csc(2) theta + cot(2) theta)parallel to del(T) (ln f)parallel to(2) + (cot(2) theta)parallel to del(perpendicular to)(ln f)parallel to(2)},
where N-T, N-perpendicular to, and N-theta are complex, totally real and proper pointwise slant submanifolds of (M) over tilde, respectively, and s = 1/2 dim N-theta. In this paper we also investigate the equality case of the inequality. Moreover, we give a non-trivial example and provide some applications of this inequality.