Metallic Structures for Tangent Bundles over Almost Quadratic ϕ-Manifolds

This paper aims to explore the metallic structure J2=pJ+qI, where p and q are natural numbers, using complete and horizontal lifts on the tangent bundle TM over almost quadratic ϕ-structures (briefly, (ϕ,ξ,η)). Tensor fields F˜ and F* are defined on TM, and it is shown that they are metallic structu...

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Veröffentlicht in:Mathematics (Basel) 2023-11, Vol.11 (22), p.4683
Hauptverfasser: Khan, Mohammad Nazrul Islam, Chaubey, Sudhakar Kumar, Fatima, Nahid, Al Eid, Afifah
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Sprache:eng
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Zusammenfassung:This paper aims to explore the metallic structure J2=pJ+qI, where p and q are natural numbers, using complete and horizontal lifts on the tangent bundle TM over almost quadratic ϕ-structures (briefly, (ϕ,ξ,η)). Tensor fields F˜ and F* are defined on TM, and it is shown that they are metallic structures over (ϕ,ξ,η). Next, the fundamental 2-form Ω and its derivative dΩ, with the help of complete lift on TM over (ϕ,ξ,η), are evaluated. Furthermore, the integrability conditions and expressions of the Lie derivative of metallic structures F˜ and F* are determined using complete and horizontal lifts on TM over (ϕ,ξ,η), respectively. Finally, we prove the existence of almost quadratic ϕ-structures on TM with non-trivial examples.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11224683