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

Year 2016, Volume: 4 Issue: 3, 105 - 115, 30.09.2016

Hasim Cayir

Abstract

The differential geometry of tangent
bundles was studied by several authors, for example: Yano and Ishihara [8], V.
Oproiu [3], A.A. Salimov [5], D. E. Blair [1] and among others. It is well
known that different structures defined on a manifold  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 Xand X in almost paracontact structure on tangent
bundle . In
addition, this results which obtained shall be studied for some special values
in almost paracontact structure.

Keywords

Tachibana Operators, Vishnevskii Operators, Almost Paracontact Structure, Horizontal Lift

References

• D.E.Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Math, 509, Springer Verlag, New York, (1976).
• S.Das, Lovejoy, Fiberings on almost r-contact manifolds, Publicationes Mathematicae, Debrecen, Hungary 43 (1993) 161-167.
• V.Oproiu, Some remarkable structures and connexions, defined on the tangent bundle, Rendiconti di Matematica 3 (1973) 6 VI.
• T.Omran, A.Sharffuddin, S.I.Husain, Lift of Structures on Manifolds, Publications de 1’Instıtut Mathematıqe, Nouvelle serie, 360 (50) (1984) 93 – 97.
• A.A.Salimov, Tensor Operators and Their applications, Nova Science Publ., New York (2013).
• S.Sasaki, On The Differantial Geometry of Tangent Boundles of Riemannian Manifolds, Tohoku Math. J., no.10(1958) 338-358.
• A.A.Salimov, H.Çayır, Some Notes On Almost Paracontact Structures, Comptes Rendus de 1’Acedemie Bulgare Des Sciences, tome 66 (3) (2013) 331-338.
• K.Yano, S.Ishihara, Tangent and Cotangent Bundles, Marcel Dekker Inc, New York (1973).