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 Mn 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 φ defines an integrable almost complex structure on M_n, its complete lift C_φ is a complex structure. The main result of the present paper is the following theorem: Let φ be an almost complex structure on a Riemannian manifold M_n. Then the complete lift C_φ of φ, when restricted to the cross-section determined by an almost analytic 1-form ω on M_n, is an almost complex structure. [ABSTRACT FROM AUTHOR]