Complete lift of Affine Connection to the Complex Tangent Bundle

Abstract

Several authors have introduced complete lift on the tangent bundle TM of a smooth manifold M using notations of complete lifts on manifold M, but no natural conjecture has been presented for study of complex
structure on tangent bundle. This demands introduction of some new construction, which we shall prefer to call the construction of complex analytic tangent bundle of a complex manifold and in brief complex
tangent bundle by TM