Geometric Mechanics on Warped Product Semi-Slant Submanifold of Generalized Complex Space Forms

Abstract

In this study, we develop a general inequality for warped product semi-slant submanifolds of type $M^n=N_T^{n_1}{\times }_f{N}_{\vartheta }^{n_2}$ in a nearly Kaehler manifold and generalized complex space forms using the Gauss equation instead of the Codazzi equation. There are several applications that can be developed from this. It is also described how to classify warped product semi-slant submanifolds that satisfy the equality cases of inequalities (determined using boundary conditions). Several results for connected, compact warped product semi-slant submanifolds of nearly Kaehler manifolds are obtained, and they are derived in the context of the Hamiltonian, Dirichlet energy function, gradient Ricci curvature, and nonzero eigenvalue of the Laplacian of the warping functions.