On almost complex structures in the cotangent bundle

E. M. Patterson and K. Yano studied vertical and complete lifts of tensor fields and connections from a manifold M(n) to its cotangent bundle T* (M(n)). Afterwards, K. Yano studied the behavior on the cross-section of the lifts of tensor fields and connections on a manifold M(n) to T* (M(n)) and proved that when phi defines an integrable almost complex structure on M(n), its complete lift (C)phi is a complex structure. The main result of the present paper is the following theorem: Let phi be an almost complex structure on a Riemannian manifold M(n). Then the complete lift (C)phi of phi, when restricted to the cross-section determined by an almost analytic 1-form omega on M(n), is an almost complex structure.