Metallic Structures on Differentiable Manifolds

In this paper, we study metallic structures, i.e. polynomial structures with the structure polynomial $Q\left(J\right)=J^2-aJ-bI$ on manifolds using the metallic ratio, which is a generalization of the Golden proportion. We investigate for integrability and parallelism conditions of metallic structures. Also, we give some properties of the metallic Riemannian metric and an example of the metallic structure.