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http://dx.doi.org/10.5666/KMJ.2021.61.4.791

Integrability of the Metallic Structures on the Frame Bundle  

Islam Khan, Mohammad Nazrul (Department of Computer Engineering, College of Computer, Qassim University)
Publication Information
Kyungpook Mathematical Journal / v.61, no.4, 2021 , pp. 791-803 More about this Journal
Abstract
Earlier investigators have made detailed studies of geometric properties such as integrability, partial integrability, and invariants, such as the fundamental 2-form, of some canonical f-structures, such as f3 ± f = 0, on the frame bundle FM. Our aim is to study metallic structures on the frame bundle: polynomial structures of degree 2 satisfying F2 = pF +qI where p, q are positive integers. We introduce a tensor field Fα, α = 1, 2…, n on FM show that it is a metallic structure. Theorems on Nijenhuis tensor and integrability of metallic structure Fα on FM are also proved. Furthermore, the diagonal lifts gD and the fundamental 2-form Ωα of a metallic structure Fα on FM are established. Moreover, the integrability condition for horizontal lift FαH of a metallic structure Fα on FM is determined as an application. Finally, the golden structure that is a particular case of a metallic structure on FM is discussed as an example.
Keywords
Horizontal lift; Vertical lift; Nijenhuis tensor; Integrability; Frame bundle;
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