Modelling with lifts of metallic structures from a Riemannian manifold to the frame bundle
Abstract
The present paper aims to study the geometric structure J2 - αJ -
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.
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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