What question did this study set out to answer?

The aim is to study the geometric structure of metallic structures on the frame bundle, defined through a new tensor field.

May 29, 2026Open Access

Modelling with lifts of metallic structures from a Riemannian manifold to the frame bundle

Key Points

The aim is to study the geometric structure of metallic structures on the frame bundle, defined through a new tensor field.
Introduced a metallic structure defined by the equation J2-α J-βI = 0 where α, β are natural numbers.
Calculated the Nijenhuis tensor and the Lie derivative associated with the metallic structure.
Investigated applications of the distribution Q on the frame bundle.
Proved theorems regarding mathematical operators on the frame bundle.
Demonstrated the existence of a metallic structure via the new tensor field.
Provided applications of the derived distributions related to the frame bundle.

Abstract

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.

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