On structures in the Semi-tangent Bundle

Abstract

The main goal of this paper is to identify some important tensor structures in the semi-tangent bundle, to provide instances of these structures and to study lift problems in these structures. The definition of almost product, almost paracomplex, almost contact and almost paracontact structural geometry in a semi-tangent bundle is covered in this paper. Using the semi-tangent bundle theory, several properties of adapted frames are shown. Furthermore, the prolongations (horizontal lifts, complete lifts and vertical lifts) of affinor fields in the semi-tangent bundle are used in this study to build almost product, almost complex and Lorentzian almost paracontact structures.