Operators Applied to Polynomial Structures on the Semi-Tangent Bundle

Investigating the Tachibana and Vishnevskii operators used on [Formula: see text] and [Formula: see text] in accordance with the almost paracontact structure in the semi-tangent bundle [Formula: see text] is the primary goal of this work. Additionally, in the almost paracontact structure, these relationships will be examined for some special vector fields. Studying the Lie derivatives of the almost paracontact structure and almost contact structure on the semi-tangent bundle [Formula: see text] with regard to [Formula: see text] and [Formula: see text] is the secondary goal of this paper.