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

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