Characterizations of the Frame Bundle Admitting Metallic Structures on Almost Quadratic ϕ -Manifolds

Mohammad Nazrul Islam Khan, Uday Chand De and Teg Alam ()
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Mohammad Nazrul Islam Khan: Department of Computer Engineering, College of Computer, Qassim University, Buraydah 51452, Saudi Arabia
Uday Chand De: Department of Pure Mathematics, University of Calcutta, 35, Ballygaunge Circular Road, Kolkata 700019, India
Teg Alam: Department of Industrial Engineering, College of Engineering, Prince Sattam bin Abdulaziz University, Al Kharj 11942, Saudi Arabia

Mathematics, 2023, vol. 11, issue 14, 1-12

Abstract: In this work, we have characterized the frame bundle F M admitting metallic structures on almost quadratic ϕ -manifolds ϕ 2 = p ϕ + q I − q η ⊗ ζ , where p is an arbitrary constant and q is a nonzero constant. The complete lifts of an almost quadratic ϕ -structure to the metallic structure on F M are constructed. We also prove the existence of a metallic structure on F M with the aid of the J ˜ tensor field, which we define. Results for the 2-Form and its derivative are then obtained. Additionally, we derive the expressions of the Nijenhuis tensor of a tensor field J ˜ on F M . Finally, we construct an example of it to finish.

Keywords: metallic structure; frame bundle; partial differential equations; almost quadratic ? -structure; 2-Form; diagonal lift; mathematical operators; nijenhuis tensor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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