Geometry of Bi-Warped Product Submanifolds of Nearly Trans-Sasakian Manifolds

In the present work, we consider two types of bi-warped product submanifolds, M = M-T x (f1) M-perpendicular to x (f2) M-phi and M = M-phi x (f1) M-T x (f2) M-perpendicular to, in nearly trans-Sasakian manifolds and construct inequalities for the squared norm of the second fundamental form. The main results here are a generalization of several previous results. We also design some applications, in view of mathematical physics, and obtain relations between the second fundamental form and the Dirichlet energy. The relationship between the eigenvalues and the second fundamental form is also established.