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Dergiler / Hagia Sophia Journal of Geometry / 2026 / Cilt: 3 Sayı: 1

Geodesics on the Cotangent Bundle with Vertical Rescaled Cheeger-Gromoll Metric

Zagane Abderrahım(University Center Ahmed Zabana-Relizane)0000-0001-9339-3787
Sayfa
1–8
Yayın Tarihi
2021-08-30
DOI
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Finally, we also construct some examples of geodesics.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we introduce the vertical rescaled Cheeger-Gromoll metric (deformation in the vertical bundle) on the cotangent bundle T*M over a Riemannian manifold (M, g) and we investigate the Levi-Civita connection of this metric.
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Temel Bulgular & Veri:We study the geodesics on the cotangent bundle with respect to the vertical rescaled Cheeger-Gromoll metric.
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Sonuç & Katkı:Finally, we also construct some examples of geodesics.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:cotangent bundles · vertical rescaled Cheeger-Gromoll metric · geodesics

Abstract

In this paper, we introduce the vertical rescaled Cheeger-Gromoll metric (deformation in the vertical bundle) on the cotangent bundle T*M over a Riemannian manifold (M, g) and we investigate the Levi-Civita connection of this metric. We study the geodesics on the cotangent bundle with respect to the vertical rescaled Cheeger-Gromoll metric. Afterward, we establish the necessary and sufficient conditions under which a curve be geodesic respect to this metric. Finally, we also construct some examples of geodesics.

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Bu Makaleye Atıf Yap

Abderrahım, Z. (2021). Geodesics on the Cotangent Bundle with Vertical Rescaled Cheeger-Gromoll Metric. Hagia Sophia Journal of Geometry, Cilt: 3 Sayı: 1, 1–8. https://ajindex.com/articles/1490451

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Kaynakça (9)

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  2. Ağca, F., & Salimov, A. A. (2013). Some notes concerning Cheeger-Gromoll metrics. Hacet. J. Math. Stat. 42(5), 533-549.
  3. Gezer, A., & Altunbas, M. (2016). On the rescaled Riemannian metric of Cheeger Gromoll type on the cotangent bundle. Hacet. J. Math. Stat. 45(2), 355-365.
  4. Ocak, F. (2019). Notes about a new metric on the cotangent bundle. Int. Electron. J. Geom. 12(2), 241-249
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  6. Salimov, A. A., & Ağca, F. (2011). Some properties of Sasakian metrics in cotangent bundles. Mediterr. J. Math. 8(2), 243-255.
  7. Sekizawa, M. (1987). Natural transformations of affine connections on manifolds to metrics on cotangent bundles. In: Proceedings of 14th Winter School on Abstract Analysis (Srni, 1986), Rend. Circ. Mat. Palermo, 14, 129-142.
  8. Yano, K., & Ishihara, S. (1973). Tangent and cotangent bundles. M. Dekker, New York.
  9. Zagane, A. (2020). A new class of metrics on the cotangent bundle. Bulletin of the Transilvania University of Brasov. Mathematics, Informatics, Physics. Series III, 13(1), 285-301.