Tangent Demet T M Üzerinde Liftlere Göre Yapıların Kovaryant Türevleri

Year 2018, Volume: 8 Issue: 1, 273 - 278, 01.01.2018

Haşim Çayır

Abstract

Tanjant demetin diferensiyel geometrisi, D. E. Blair Blair 1976 , V. Oproiu Oproiu 1973 , A. Salimov Salimov 2013 , Yano ve Ishihara 1973 ve diğer birçok bilim adamları tarafından çalışıldı. Bir manifold üzerinde tanımlanan farklı yapılar, onun tanjant demeti üzerindeki aynı tip yapılara taşınabilindiği bilinmektedir. Bizim bu çalışmadaki amacımız tanjant demet üzerinde almost kontakt yapı ve almost parakontakt yapıların XC, XV ve XH ye göre kovaryant türevlerini hesaplamaktır

Keywords

Almost kontakt yapı, Almost parakontakt yapı, Covariant türev, Horizontal lift

Covarient Derivatives of Structures with Respect to Lifts on Tangent Bundle

Abstract

The differential geometry of tangent bundles was studied by several authors, for example: D. E. Blair Blair 1976 , V. Oproiu Oproiu 1973 , A. Salimov Salimov 2013 , Yano and Ishihara 1973 and among others. It is well known that differant structures defined on a manifold can be lifted to the same type of structures on its tangent bundle. Our goal is to study covariant derivatives of almost contact structure and almost paracontact structure with respect to and on tangent bundle

Keywords

Almost contact structure, Almost paracontact structure, Covariant derivative, Horizontal lift, XC and XH on tangent bundle T M

References

• Blair, DE. 1976. Contact Manifolds in Riemannian Geometry, Lecture Notes in Math. 509, Springer Verlag, New York.
• Çayır, H. 2015. Some Notes on Lifts of Almost Paracontact Structures. Am. Rev. of Math. and Stat., 3(1): 52-60 .
• Çayır, H. 2016a. Lie derivatives of Almost Contact Structure and Almost Paracontact Structure with respect to XV and XC on Tangent Bundle T(M). Proc. of the Inst. of Math. and Mech., 42(1): 38-49.
• Çayır, H. 2016b. Tachibana and Vishnevskii Operators Applied to XV and XC in Almost Paracontact Structure on Tangent Bundle T(M). Ordu Üniv. Bil. ve Tek. Der., 6(1): 67-82.
• Çayır, H. 2016c. Tachibana and Vishnevskii Operators Applied to
• XV and XH and in Almost Paracontact Structure on Tangent
• Bundle T(M). New Tr. in Math. Sci., 4(3): 105-115.
• Çayır, H., Köseoğolu, G. 2016. Lie Derivatives of Almost Contact Structure and Almost Paracontact Structure With Respect to XCand XV on Tangent Bundle T(M). New Tr. in Math. Sci., 4(1): 153-159.