Complete lift of a structure satisfying FK ￠ ’( ￠ ’)K+1F=0

The idea of f-structure manifold on a differentiable manifold was initiated and developed by Yano [1], Ishihara and Yano [2], Goldberg [3] and among others. The horizontal and complete lifts from a differentiable manifold Mn of class C ￠ to its cotangent bundles have been studied by Yano and Patterson [4,5]. Yano and Ishihara [6] have studied lifts of an f-structure in the tangent and cotangent bundles. The purpose of this paper is to obtain integrability conditions of a structure satisfying FK ￠ ’( ￠ ’)K+1F=0 and FW ￠ ’( ￠ ’)W+1F ￠ ‰ 0 for 1 Keywords tangent bundle --- complete lift --- F-structure --- integrability --- distributions.