Abstract
Earlier investigators have made detailed studies of geometric properties such as integrability, partial integrability, and invariants, such as the fundamental 2-form, of some canonical f-structures, such as f(3)+/- f = 0, on the frame bundle FM. Our aim is to study metallic structures on the frame bundle: polynomial structures of degree 2 satisfying F-2 = pF +qI - where p,q are positive integers. We introduce a tensor field F-alpha , alpha = 1, 2..., n on FM show that it is a metallic structure. Theorems on Nijenhuis tensor and integrability of metallic structure F-alpha on FM are also proved. Furthermore, the diagonal lifts g(D) and the fundamental 2-form Omega(alpha) of a metallic structure F-alpha on FM are established. Moreover, the integrability condition for horizontal lift F-alpha(H) of a metallic structure F-alpha on FM is determined as an application. Finally, the golden structure that is a particular case of a metallic structure on FM is discussed as an example.