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Journals / International Electronic Journal of Geometry / 2026 / Volume: 19 Issue: 2

Geometric Properties of a Horizontally Deformed Cheeger-Gromoll Metric on the Tangent Bundle

Teğet Demet Üzerinde Yatay Olarak Deforme Edilmiş Cheeger–Gromoll Metriğinin Geometrik Özellikleri

Bel Mokhtar Bentadj(University of Naama)0009-0004-9433-3080
Abderrahım Zagane(Ahmed Zabana University-Relizane)0000-0001-9339-3787
Fethi Latti(University of Naama)0009-0004-3158-5707
Pages
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Publication Date
2026-10-25
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AI Summary & Key Takeaways

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

Moreover, we examined the geometry of a hypersurface embedded in the tangent bundle, providing a detailed analysis of its intrinsic structure, induced Levi--Civita connection, and associated curvature tensors.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce a novel horizontally deformed Cheeger--Gromoll metric on the tangent bundle of a Riemannian manifold, thereby enlarging the spectrum of invariant metrics available in this context.
📊
Key Findings & Data:A systematic analysis is performed on the geometric characteristics engendered by this metric, yielding explicit expressions for the Levi--Civita connection and the full array of curvature tensors.
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Conclusion & Impact:Moreover, we examined the geometry of a hypersurface embedded in the tangent bundle, providing a detailed analysis of its intrinsic structure, induced Levi--Civita connection, and associated curvature tensors.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Tangent bundle · horizontally deformed Cheeger--Gromoll metric · curvature tensor

Abstract

We introduce a novel horizontally deformed Cheeger--Gromoll metric on the tangent bundle of a Riemannian manifold, thereby enlarging the spectrum of invariant metrics available in this context. A systematic analysis is performed on the geometric characteristics engendered by this metric, yielding explicit expressions for the Levi--Civita connection and the full array of curvature tensors. Moreover, we examined the geometry of a hypersurface embedded in the tangent bundle, providing a detailed analysis of its intrinsic structure, induced Levi--Civita connection, and associated curvature tensors.

Özet

Bu çalışmada, bir Riemannyen manifoldun teğet demeti üzerinde yeni bir yatay olarak deforme edilmiş Cheeger–Gromoll metriği tanıtılarak, bu bağlamda mevcut olan değişmez metriklerin yelpazesi genişletilmektedir. Söz konusu metrik tarafından ortaya çıkarılan geometrik özellikler sistematik bir biçimde incelenmiş; Levi–Civita bağlantısı ile tüm eğrilik tensörleri için açık ifadeler elde edilmiştir. Ayrıca, teğet demet içerisine gömülmüş bir hiperyüzeyin geometrisi ele alınarak, bu hiperyüzeyin içsel yapısı, indüklenen Levi–Civita bağlantısı ve buna karşılık gelen eğrilik tensörleri ayrıntılı biçimde analiz edilmiştir.

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Cite This Article

Bentadj, B. M., Zagane, A., Latti, F. (2026). Geometric Properties of a Horizontally Deformed Cheeger-Gromoll Metric on the Tangent Bundle. International Electronic Journal of Geometry, Volume: 19 Issue: 2. https://doi.org/10.36890/iejg.1871406

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References (16)

  1. Abbassi, M. T. K., Sarih, M.: On Natural Metrics on Tangent Bundles of Riemannian Manifolds. Arch. Math. 41 (1), 71–92 (2005).
  2. Dombrowski, P.: On the Geometry of the tangent bundle. J. Reine Angew. Math. 210 (1962), 73–88. https://doi.org/10.1515/crll.1962.210.73
  3. Gezer, A.: On the Tangent Bundle with Deformed Sasaki Metric. Int. Electron. J. Geom. 6(2), 19–31 (2013).
  4. Gezer, A., Altunbaş, M.: On the rescaled Riemannian metric of Cheeger Gromoll type on the cotangent bundle. Hacet. J. Math. Stat. 45 (2), 355–365 (2016).
  5. Gudmundsson, S., Kappos, E.: On the Geometry of the Tangent Bundle with the Cheeger–Gromoll Metric. Tokyo J. Math. 25 (1), 75–83 (2002). https://doi.org/10.1386/tjm/1244208938
  6. Musso, E., Tricerri, F.: Riemannian Metrics on Tangent Bundles. Ann. Mat. Pura Appl. 150 (4), 1–19 (1988). https://doi.org/10.1007/BF01761461
  7. Salimov, A. A., Gezer, A., Akbulut, K.: Geodesics of Sasakian metrics on tensor bundles. Mediterr. J. Math. 6 (2), 135–147 (2009). https://doi.org/10.1007/s00009-009-0001-z
  8. Salimov, A. A., Kazimova, S.: Geodesics of the Cheeger–Gromoll Metric. Turk. J. Math. 33, 99–105 (2009).
  9. Sasaki, S.: On the differential geometry of tangent bundles of Riemannian manifolds II. Tohoku Math. J. (2) 14 (2), 146–155 (1962). https://doi.org/10.2748/tmj/1178244169
  10. Wang, J., Wang, Y.: On the geometry of tangent bundles with the rescaled metric. arXiv:1104.5584v1 (2011). https://doi.org/10.48550/arXiv.1104.5584
  11. Yano, K., Ishihara, S.: Tangent and cotangent bundles. Marcel Dekker, Inc. New York (1973).
  12. Zagane, A.: Vertical rescaled Berger deformation metric on the tangent bundle. Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 41 (4), 166–180 (2021).
  13. Zagane, A.: On the Geometry of Tangent Bundle and Unit Tangent Bundle with Deformed-Sasaki Metric. Int. Electron. J. Geom. 16 (1), 132–146 (2023). https://doi.org/10.36890/IEJG.1182395
  14. Zagane, A.: Some results of harmonicity on tangent bundles with $\varphi$-Sasakian Metrics over para-Kähler-Norden manifold. Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 49 (2), 295–311 (2023). https://doi.org/10.30546/2409-4994.2023.49.2.295
  15. Zagane, A.: Some Almost $B$-Structures on the Tangent Bundle Equipped with a Vertical Rescaled Metric. Turk. J. Math. Comput. Sci. 18 (1), 184–198 (2024). https://doi.org/10.47000/tjmcs.1458966
  16. Zagane, A., Latti, F.: Study of some harmonicity problems concerning the rescaled Sasaki metric. Int. J. Maps Math. 8 (1), 160–176 (2025).