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Journals / 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
Pages
1–8
Publication Date
2021-08-30
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we also construct some examples of geodesics.

📌 3 Key Takeaways

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Objective & Hypothesis: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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Key Findings & Data:We study the geodesics on the cotangent bundle with respect to the vertical rescaled Cheeger-Gromoll metric.
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Conclusion & Impact:Finally, we also construct some examples of geodesics.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables: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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Cite This Article

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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References (9)

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