Geometric classification of warped product submanifolds of nearly Kaehler manifolds with a slant fiber

Abstract

There are two types of warped product pseudo-slant submanifolds, M-theta x (f) M-perpendicular to and M-perpendicular to x (f) M-theta, in a nearly Kaehler manifold. We derive an optimization for an extrinsic invariant, the squared norm of second fundamental form, on a nontrivial warped product pseudo-slant submanifold M-perpendicular to x (f) M-theta in a nearly Kaehler manifold in terms of a warping function and a slant angle when the fiber M-theta is a slant submanifold. Moreover, the equality is verified for depending on what M-theta and M-perpendicular to are, and also we show that. if the equality holds, then M-perpendicular to x (f) M-theta is a simply Riemannian product. As applications, we prove that the warped product pseudo-slant submanifold has the finite Kinetic energy if and only if M-perpendicular to x (f) M-theta is a totally real warped product submanifold.