This paper consists of two main sections. In the first part, we find the integrability conditions by calculating Nijenhuis tensors of the horizontal lifts of F (2K + S, S)−structure Satisfying F 2K+S + F S = 0. Later, we get the results of Tachibana operators applied to vector and covector fields according to the horizontal lifts of F (2K + S, S)−structure in cotangent bundle T * (M n). Finally, we have studied the purity conditions of Sasakian metric with respect to the horizontal lifts of the structure. In the second part, all results obtained in the first section were obtained according to the complete and horizontal lifts of F (2K + S, S)−structure in tangent bundle T (M n).
This paper consist of three main sections. In the …rst part, we obtain the complete lifts of the Fa(5; 1) structure on tangent bundle. We have also obtained the integrability conditions by calculating the Nijenhuis tensors of the complete lifts of Fa(5; 1) structure. Later we get the conditions of to be the almost holomor…c vector …eld with respect to the complete lifts of Fa(5; 1) structure. Finally, we obtained the results of the Tachibana operator applied to the vector …elds with respect to the complete lifts of Fa(5; 1) structure on tangent bundle. In the second part, all results obtained in the …rst section investigated according to the horizontal lifts of Fa(5; 1) structure in tangent bundle T (M n ). In …nally section, all results obtained in the …rst and second section were investigated according to the horizontal lifts of the Fa(5; 1) structure in cotangent bundle T (M n ).
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