Integrability and Lie Derivatives of Metallic Structures Over Framed AQ Ï•-Manifolds With Modeling

Dalal Alhwikem, Teg Alam and Mohammad Nazrul Islam Khan

Journal of Mathematics, 2026, vol. 2026, 1-8

Abstract: This paper aims to study the Lie derivative with respect to the vector field Y in n-dimensional differentiable manifold M and investigate certain conditions for vertical and complete lifts YV and YC of Y by means of mathematical operators is almost analytic with respect to the metallic structure F˜ in the tangent bundle TM over almost quadratic ϕ-structures ϕ,δ,γ (in short, AQ ϕ-structures). Next, a framed AQ ϕ-structure ϕ,δx,γx is defined in M and proved that a (1,1) tensor field F˜ in TM is a metallic structure in TM over ϕ,δx,γx. Furthermore, the integrability conditions of the metallic structure F˜ in TM over ϕ,δx,γx are modeled. Finally, the geometrical properties of the Lie derivative with respect to F˜ in TM over ϕ,δx,γx are discussed.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:7848471

DOI: 10.1155/jom/7848471

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