Some basic inequalities on Riemannian manifolds equipped with metallic structure

In the current research, we develop sharp inequalities including generalized normalized δ-Casorati curvatures for several submanifolds of Riemannian manifolds endowed with metallic structures. For these submanifolds in the same ambient space form, we have also looked into generalized Wintgen inequalities. Additionally, submanifolds for which the equality cases hold are described as well.