Ricci curvature of semi-slant warped product submanifolds in generalized complex space forms

Abstract

The objective of this paper is to achieve the inequality for Ricci curvature of a semi-slant warped product submanifold isometrically immersed in a generalized complex space form admitting a nearly Kaehler structure in the expressions of the squared norm of mean curvature vector and warping function. In addition, the equality case is likewise discussed. We provide numerous physical applications of the derived inequalities. Later, we proved that under a certain condition the base manifold $ N_T^{n_1} $ is isometric to a $ n_1 $-dimensional sphere $ S^{n_1}(\frac{\lambda_1}{n_1}) $ with constant sectional curvature $ \frac{\lambda_1}{n_1}. $

Keywords

• ricci curvature
• laplacian
• hamiltonian
• dirichlet energy