Proposed theorems for lifts of the extended almost complex structures on the complex manifold

It is well known that the tensor field [Formula: see text] of type on manifold an almost complex structure if identity and called manifold. Let k M be order extended text]. A This paper aims to study higher complete vertical lifts structures M. The proposed theorems Nijenhuis are proved. Also, a introduced shows it structure. Furthermore, Lie derivative concerning higher-order studied basic results analytic vector investigated. Finally, for more detailed explanation better understanding M, proving metallic golden structure, which also carried out.