Bounds for Generalized Normalized delta-Casorati Curvatures for Submanifolds in Generalized (kappa, mu)-space Forms

In this paper, we prove the optimal inequalities for the generalized normalized delta-Casorati curvature and the normalized scalar curvature for different submanifolds in generalized (kappa, mu)-space forms. The proof is based on an optimization procedure involving a quadratic polynomial in the components of the second fundamental form. We also characterize the submanifolds on which equalities hold.