Geodesics and Torsion Tensor according to g-lift of Riemannian Connection on Cotangent Bundle

Year 2020, Volume: 10 Issue: 1, 595 - 600, 01.03.2020

Rabia Çakan Akpınar

https://doi.org/10.21597/jist.622820

Abstract

n this study, the geodesics and torsion tensor according to g-lift of Riemannian
connection  on cotangent bundle 𝑇∗𝑀 are investigated. Firstly, using the components of g-lift of
Riemannian connection  on cotangent bundle 𝑇∗𝑀 the components of torsion tensor according to glift
of Riemannian connection  are obtained. So the torsion tensor according to g-lift of Riemannian
connection  are determined. Finally, geodesics on cotangent bundle 𝑇∗𝑀 according to g-lift of
Riemannian connection  are studied.

Keywords

Cotangent Bundle, Connection, Torsion Tensor, Geodesic, g-lift

Kotanjant Demette Riemann Konneksiyonun g-liftine göre Burulma Tensörü ve Geodezikler

Abstract

Bu çalışmada, 𝑇∗𝑀 kotanjant demette Riemann konneksiyonun g-liftine göre burulma tensörü
ve geodezikler incelenir. İlk olarak, 𝑇∗𝑀 kotanjant demet üzerindeki Riemann konneksiyonun g-liftinin
bileşenleri kullanılarak  Riemann konneksiyonun g-liftine göre burulma tensor bileşenleri elde edilir.
Böylece  Riemann konneksiyonun g-liftine göre burulma tensörü belirlenir. Son olarak,  Riemann
konneksiyonun g-liftine göre 𝑇∗𝑀 kotanjant demet üzerindeki geodezikler çalışılır.

Keywords

Kotanjant Demet, Konneksiyon, Burulma Tensörü, Jeodezik, g-lift

References

• Cakan R, Akbulut K, Salimov A, 2016. Musical Isomorphisms and Problems of Lifts. Chinese Annals of Mathematics Series B, 37(3): 323-330.
• Cakan R, Kemer E, 2019. The g-lift of Affine Connection in the Cotangent Bundle. Punjab University Journal of Mathematics, 51(11): 53-62.
• Cengiz N, Salimov AA, 2002. Geodesics in the Tensor Bundle of Diagonal Lİfts. Haccettepe Journal of Mathematics and Statistics, 31: 1-11.
• Çayır H, 2019a. On Integrability Conditions, Operators and the Purity Conditions of the Sasakian Metric with respect to lifts of structure on the cotangent bundle. Turkish Journal of Mathematics, 43(1): 186-198.
• Çayır H, 2019b. Derivatives of Sasakian metric on Cotangent Bundle. Communications Faculty Sciences University of Ankara Series A1-Mathematics and Statistics, 68(1): 751-761.
• Druta Romaniuc SL, 2012. Natural Diagonal Riemannian Almost Product and Para-Hermitian Cotangent Bundles. Czechoslovak Mathematical Journal, 62(4): 937-949.
• Kurek J, Mikulski WM, 2013. The Natural Operators Lifting Connections to Tensor Powers of the Cotangent Bundle. Miskolc Mathematical Notes, 14: 517-524.
• Mağden A, Salimov AA, 2004. Geodesics for Complete Lifts of Affine Connections in Tensor Bundles. Applied Mathematics and Computation, 151: 863-868.
• Salimov AA, Cakan R, 2017. Problems of lifts. Proceeding of the Institute of Mathematics and Mechanics, 43(1): 161-170.
• Mok KP, 1977. Metrics and Connections on the Cotangent Bundles. Kodai Mathematical Seminar Reports, 28: 226-238.
• Yano K, Ishihara S, 1973. Tangent and Cotangent Bundles. Marcel Dekker, New York.
• Yano K, Patterson EM, 1967. Vertical and Complete Lifts from a manifold to its Cotangent Bundle. Journal of the Mathematical Society of Japan, 19: 91-113.