Geometric inequalities of bi-warped product submanifold in generalized complex space form

Abstract

In this article, we obtain some inequalities for the bi-warped product submanifold of nearly-Kähler manifold which is expressed in terms of Laplacian, gradient, slant coefficient, and second fundamental form. Our inequality generalizes the inequalities of [1,20]. We also compute the Dirichlet energy and first eigenvalue of the Laplacian of warping functions.