Abstract
It is well known that the prolongation of an almost complex structure from a manifold M to the tangent bundle of order r on M is also an almost complex structure if it is integrable. The general quadratic structure F-2 = alpha F + beta I is a generalization of an almost complex structure where alpha = 0, beta = -1. The purpose of this paper is to characterize a metallic structure defined by the general quadratic structure F-2 = alpha F + beta I, alpha, beta is an element of N, where N is the set of natural numbers. We show that the r lift of the metallic structure F in the tangent bundle of order r is also a metallic structure. Furthermore, we deduce a theorem on the projection tensor in the tangent bundle of order r. Moreover, prolongations of G-structures immersed in the metallic structure to the tangent bundle of order r and 2 are discussed. Finally, we construct examples of metallic structures that admit an almost para contact structure on the tangent bundle of order 3 and 4.