Horizontal Lifts of Tensor Fields to the Complex Cotangent Bundle

Abstract

Several authors have introduced horizontal lifts of the cotangent bundle 2n of a smooth manifold M using notations of horizontal lifts of tensor field on manifold M, but no natural conjecture has been presented for study of complex structure on cotangent bundle. This demands introduction of some new construction, which we shall prefer to call the construction of complex analytic cotangent bundle of a complex manifold and in brief complex cotangent