Abstract
It has been found that an almost complex structure of a contact metric manifold on frame bundle (FM, g(D), J) is an almost Hermitian manifold. The derivative and coderivative of the Kahler form of the almost Hermitian structure (g(D), J) are determined on frame bundle. An almost complex structure is a particular case of the polynomial structure of degree 2 satisfying J(2) = pJ + qI, where p = 0, q = -1. However, the main contribution of this paper is that the results by applying the p, q as positive numbers then it satisfies the condition on J(2) = pJ + qI and termed as metallic structure. Furthermore, a tensor field (J) over tilde J is introduced on a frame bundle FM which proves that it is metallic structure on FM. The proposed theorem shows that the diagonal lift g(D) of a Riemannian metric g is a metallic Riemannian metric on FM. The derivative and coderivative of 2-form F of metallic Riemannian structure on F Mare calculated. Moreover, the Nijenhuis tensor of tensor field (J) over tilde is determined. Finally, a locally metallic Riemannian manifold (FM, J(H), g(D)) is described as an application. (C) 2021 Elsevier Ltd. All rights reserved.