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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
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.

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.

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

Year 2020, Volume: 10 Issue: 1, 595 - 600, 01.03.2020
https://doi.org/10.21597/jist.622820

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.

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.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Matematik / Mathematics
Authors

Rabia Çakan Akpınar 0000-0001-9885-6373

Publication Date March 1, 2020
Submission Date September 20, 2019
Acceptance Date November 28, 2019
Published in Issue Year 2020 Volume: 10 Issue: 1

Cite

APA Çakan Akpınar, R. (2020). Geodesics and Torsion Tensor according to g-lift of Riemannian Connection on Cotangent Bundle. Journal of the Institute of Science and Technology, 10(1), 595-600. https://doi.org/10.21597/jist.622820
AMA Çakan Akpınar R. Geodesics and Torsion Tensor according to g-lift of Riemannian Connection on Cotangent Bundle. J. Inst. Sci. and Tech. March 2020;10(1):595-600. doi:10.21597/jist.622820
Chicago Çakan Akpınar, Rabia. “Geodesics and Torsion Tensor According to G-Lift of Riemannian Connection on Cotangent Bundle”. Journal of the Institute of Science and Technology 10, no. 1 (March 2020): 595-600. https://doi.org/10.21597/jist.622820.
EndNote Çakan Akpınar R (March 1, 2020) Geodesics and Torsion Tensor according to g-lift of Riemannian Connection on Cotangent Bundle. Journal of the Institute of Science and Technology 10 1 595–600.
IEEE R. Çakan Akpınar, “Geodesics and Torsion Tensor according to g-lift of Riemannian Connection on Cotangent Bundle”, J. Inst. Sci. and Tech., vol. 10, no. 1, pp. 595–600, 2020, doi: 10.21597/jist.622820.
ISNAD Çakan Akpınar, Rabia. “Geodesics and Torsion Tensor According to G-Lift of Riemannian Connection on Cotangent Bundle”. Journal of the Institute of Science and Technology 10/1 (March 2020), 595-600. https://doi.org/10.21597/jist.622820.
JAMA Çakan Akpınar R. Geodesics and Torsion Tensor according to g-lift of Riemannian Connection on Cotangent Bundle. J. Inst. Sci. and Tech. 2020;10:595–600.
MLA Çakan Akpınar, Rabia. “Geodesics and Torsion Tensor According to G-Lift of Riemannian Connection on Cotangent Bundle”. Journal of the Institute of Science and Technology, vol. 10, no. 1, 2020, pp. 595-00, doi:10.21597/jist.622820.
Vancouver Çakan Akpınar R. Geodesics and Torsion Tensor according to g-lift of Riemannian Connection on Cotangent Bundle. J. Inst. Sci. and Tech. 2020;10(1):595-600.