On the lifts of F_{a}(5,1)-structure on tangent and cotangent bundle

Abstract

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 ).