Ricci curvature of contact CR-warped product submanifolds in generalized Sasakian space forms admitting nearly Sasakian structure

Abstract

The objective of this paper is to achieve the inequality for Ricci curvature of a contact CR-warped product submanifold isometrically immersed in a generalized Sasakian space form admitting a nearly Sasakian structure in the expressions of the squared norm of mean curvature vector and warping function. In addition, the equality case is likewise discussed. 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

• contact cr-submanifolds
• generalized sasakian space form
• ricci curvature
• laplacian
• warped product