The present paper aims to study the geometric structure J2-α J-βI = 0, α, β are natural numbers, is named as a metallic structure on the frame bundle. It is further demonstrated to have a metallic structure by the definition of a new tensor field J concerning ‘the horizontal’ and ‘vertical lifts’ on the frame bundle. Furthermore, certain theorems on the mathematical operators on the frame bundle are proved. Moreover, the Nijenhuis tensor and the Lie derivative of a metallic structure J on the frame bundle are calculated. Finally, an application on the distribution Q on the frame bundle is investigated.
Khan et al. (Wed,) studied this question.