On the Lifts of F(2K + S; S)􀀀Structure Satisfying F2K+S + FS = 0; (F 6= 0; K 1 1; S 1 1) on Cotangent and Tangent Bundle

Abstract

This paper consists of two main sections. In the first part, we find the integrability conditions bycalculating Nijenhuis tensors of the horizontal lifts of F(2K + S; S)􀀀structure Satisfying F2K+S +FS = 0. Later, we get the results of Tachibana operators applied to vector and covector fieldsaccording to the horizontal lifts of F(2K + S; S)􀀀structure in cotangent bundle T(Mn). Finally,we have studied the purity conditions of Sasakian metric with respect to the horizontal lifts of thestructure. In the second part, all results obtained in the first section were obtained according to thecomplete and horizontal lifts of F(2K + S; S)􀀀structure in tangent bundle T(Mn).