Tachibana and Vishnevskii operators applied to X$^{V}$ and $X^{H}$ in almost paracontact structure on tangent bundle $T(M)$

Abstract

Abstract:The differential geometry of tangent bundles was studied by several authors, for example: Yano and Ishihara [8]and among others. It is well known that different structures defined on a manifold M can be lifted to the same type of structures on its tangent bundle. In addition, several authors was studied on operators too, for example: A.A. Salimov [5]. Our goal is to study Tachibana and Vishnevskii Operators Applied to X V and X H in almost paracontact structure on tangent bundle T (M). In addition, this results which obtained shall be studied for some special values in almost paracontact structure.

Operators Applied to Lifts with Respect to the Diagonal Lifts of Affinor Fields Along a Cross-Section on $T_{q}^{p}(M)$

“…the module of all pure tensor fields of type (r, s) on M n according to the affinor field φ [2,3,9,12](see [10] for applied to pure tensor field).…”

“…for any X, Y ∈ ℑ 1 0 (M n ). Then we can consider a new operator by a Vishnevskii operator or ψ φ −operator on M n , we shall mean a map ψ φ : * ℑ(M n ) → ℑ(M n ), which satisfies conditions a), b), c), e) of definition 2.1 and the condition (d ′ ) [2,3,8,9].…”

On Complete, Horizontal and Vertical Lifts From a Manifold With fλ(6,4) Structure to Its Cotangent Bundle

“…Li and Krupka [7] discussed the properties of tangent bundles. Cayir [1], [2] and [3] studied lifts of F ν+1 , λ 2 F ν−1 structure.…”