@article{Khan2022, 
author = {Mohammad Nazrul Islam Khan and Uday Chand De},
title = {Liftings of metallic structures to tangent bundles of order    r},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {7888-7897},
keywords = {lifts, metallic structure, integrability, projection tensor, prolongation},
url = {https://www.sciopen.com/article/10.3934/math.2022441},
doi = {10.3934/math.2022441},
abstract = {It is well known that the prolongation of an almost complex structure from a manifold    M to the tangent bundle of order    r on    M is also an almost complex structure if it is integrable. The general quadratic structure        F    2    =  α  F  +  β  I is a generalization of an almost complex structure where    α  =  0  ,    β  =  −  1. The purpose of this paper is to characterize a metallic structure defined by the general quadratic structure        F    2    =  α  F  +  β  I  ,    α  ,  β  ∈      N  , where        N   is the set of natural numbers. We show that the    r-lift of the metallic structure    F in the tangent bundle of order    r is also a metallic structure. Furthermore, we deduce a theorem on the projection tensor in the tangent bundle of order    r. Moreover, prolongations of    G-structures immersed in the metallic structure to the tangent bundle of order    r and 2 are discussed. Finally, we construct examples of metallic structures that admit an almost para contact structure on the tangent bundle of order 3 and 4.}
}