Optimal inequalities involving Casorati curvatures for Riemannian maps to nearly Kaehler manifolds

We establish a general inequality and optimal inequalities involving the normalized Casorati curvatures and the generalized normalized Casorati curvatures within the horizontal space of a Riemannian map from a Riemannian manifold to a nearly Kaehler manifold with a constant holomorphic sectional curvature. Riemannian maps serve as generalizations of isometric immersions and Riemannian submersions. Consequently, we extend these inequalities to encompass Riemannian submanifolds within nearly Kaehler manifolds with a constant holomorphic sectional curvature.