Metallic Structures for Tangent Bundles over Almost Quadratic ϕ -Manifolds

Mohammad Nazrul Islam Khan (), Sudhakar Kumar Chaubey, Nahid Fatima and Afifah Al Eid
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Mohammad Nazrul Islam Khan: Department of Computer Engineering, College of Computer, Qassim University, Buraydah 51452, Saudi Arabia
Sudhakar Kumar Chaubey: Section of Mathematics, Department of Information Technology, University of Technology and Applied Sciences, P.O. Box 77, Shinas 324, Oman
Nahid Fatima: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Afifah Al Eid: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

Mathematics, 2023, vol. 11, issue 22, 1-16

Abstract: This paper aims to explore the metallic structure J 2 = p J + q I , where p and q are natural numbers, using complete and horizontal lifts on the tangent bundle T M over almost quadratic ϕ -structures (briefly, ( ϕ , ξ , η ) ). Tensor fields F ˜ and F * are defined on T M , and it is shown that they are metallic structures over ( ϕ , ξ , η ) . Next, the fundamental 2-form Ω and its derivative d Ω , with the help of complete lift on T M 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 T M over ( ϕ , ξ , η ) , respectively. Finally, we prove the existence of almost quadratic ϕ -structures on T M with non-trivial examples.

Keywords: metallic structure; tangent bundle; partial differential equations; nijenhuis tensor; mathematical operators; lie derivatives (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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