Abstract
We study bi-warped product submanifolds of nearly Kaehler manifolds which are the natural extension of warped products. We prove that every bi-warped product submanifold of the form M = M-T x f(1) M-perpendicular to x f(2) M-theta in a nearly Kaehler manifold satisfies the following sharp inequality:
parallel to h parallel to(2) >= 2p parallel to del(In f(1))parallel to(2) + 4q (1 + 10/9 cot(2)theta) parallel to del(In f(2))parallel to(2),
where p = dim M-perpendicular to, q = 1/2 dim M-theta, and f(1), f(2) are smooth positive functions on M-T. We also investigate the equality case of this inequality. Further, some applications of this inequality are also given.