Metallic Structures on Product Manifolds and Ricci-Chen Inequalities

In this study, we discuss metallic structures on product manifolds and derive the Chen-Ricci inequalities for remarkable submanifolds determined by the behaviour of their tangent bundles with regard to the action of the metallic structure in a locally decomposable metallic Riemannian manifold whose components are spaces of constant curvature. Moreover, the equality cases are considered in order to characterize these submanifolds.