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On integrability conditions, operators, and the purity conditions of the Sasakian metric with respect to lifts of Fλ(7, 1)-structure on the cotangent bundle

There are many structures in the cotangent bundle. These include the complete and horizontal lifts of the Fλ(7, 1) -structure. The Fλ(7, 1) -structure was first extended in M n to T ∗(M n) by Das, Nivas, and Pathak. Later, the horizontal and complete lift of the Fa(K, 1) -structure in the tangent bundle was given by Prasad and Chauhan. This paper consists of two main sections. In the first part, we find the integrability conditions by calculating Nijenhuis tensors of the complete lifts of the Fλ(7, 1) -structure. Later, we get the results of the Tachibana operators applied to vector and covector fields according to the complete lifts of the Fλ(7, 1) -structure in the cotangent bundle T ∗(Mn) . Finally,we study the purity conditions of the Sasakian metric with respect to the complete lifts of the Fλ(7, 1) -structure. In thesecond part, all results obtained in the first section are obtained according to the horizontal lifts of the Fλ(7, 1) -structure in cotangent bundle T ∗(Mn) .

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