On the Integrability Conditions and Operators of the F((K + 1); (K 􀀀 1))􀀀 Structure Satisfying FK+1 + FK􀀀1 = 0; (F 6= 0; K 1 2) on Cotangent Bundle and Tangent Bundle

Abstract

This paper consists of two main sections. In the first part, we find the integrability conditions ofthe horizontal lifts of F((K + 1); (K 􀀀 1))􀀀structure satisfying FK+1 + FK􀀀1 = 0; (F 6= 0; K 1 2).Later, we get the results of Tachibana operators applied to vector and covector fields according tothe horizontal lifts of F((K + 1); (K 􀀀 1))􀀀structure in cotangent bundle T(Mn). Finally, we havestudied 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 completeand horizontal lifts of the structure in tangent bundle T(Mn).