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

The objective of this paper is to achieve the inequality for Ricci curvature a contact CR-warped product submanifold isometrically immersed in generalized Sasakian space form admitting trans-Sasakian structure expressions squared norm mean vector and warping function. We provide numerous physical applications derived inequalities. Finally, we prove that under certain condition base manifold isometric sphere with constant sectional curvature.