Geeta Verma, Prashant K. Shukla

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The present paper aims to investigate `the horizontal lift' of $J$ satisfying $J^2-J-I=0$ and demonstrate its status as a type of golden structure. The Nijenhuis tensor $N^\ast$ of the horizontal lift $J^H$ on the tangent bundle is determined. Also, a tensor field $\tilde{J}$ of type (1,1) is studied and shown to be golden structure on the tangent bundle. Furthermore, several conclusions regarding the Nijenhuis tensor and the Lie derivative of the golden structure $\tilde{J}$ on the tangent bundle are deduced. Moreovber, a study is done on the golden structure $\tilde{J}$ on the tangent bundle that is equipped with projection operators $\tilde{l}$ and $\tilde{m}$. Finally, we construct an example of it.


golden structure, tangent bundle, vertical lift, horizontal lift, almost analytic vector eld, projection tensor, Nijenhuis tensor, Lie derivative

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DOI: https://doi.org/10.22190/FUMI221012007V


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