SavedAdd your journal

Journals / International Electronic Journal of Geometry / 2026 / Volume: 14 Issue: 1

Berger Type Deformed Sasaki Metric and Harmonicity on the Cotangent Bundle

Abderrahim Zagane(University Center Ahmed Zabana-Relizane)0000-0001-9339-3787
Pages
—
Publication Date
2021-04-15
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

We also construct some examples of harmonic vector fields. we also study the harmonicity of a map between a Riemannian manifold and a cotangent bundle of another Riemannian manifold and vice versa.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce the Berger type deformed Sasaki metric on the cotangent bundle $T^{\ast}M$ over an anti-paraKähler manifold $(M, \varphi, g)$.
📊
Key Findings & Data:We establish a necessary and sufficient conditions under which a covector field is harmonic with respect to the Berger type deformed Sasaki metric.
💡
Conclusion & Impact:We also construct some examples of harmonic vector fields. we also study the harmonicity of a map between a Riemannian manifold and a cotangent bundle of another Riemannian manifold and vice versa.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cotangent bundles · horizontal lift and vertical lift · Berger type deformed Sasaki metric

Abstract

In this paper, we introduce the Berger type deformed Sasaki metric on the cotangent bundle $T^{\ast}M$ over an anti-paraKähler manifold $(M, \varphi, g)$. We establish a necessary and sufficient conditions under which a covector field is harmonic with respect to the Berger type deformed Sasaki metric. We also construct some examples of harmonic vector fields. we also study the harmonicity of a map between a Riemannian manifold and a cotangent bundle of another Riemannian manifold and vice versa.

🔖

Cite This Article

Zagane, A. (2021). Berger Type Deformed Sasaki Metric and Harmonicity on the Cotangent Bundle. International Electronic Journal of Geometry, Volume: 14 Issue: 1. https://doi.org/10.36890/iejg.793530

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  1. Ağca, F.: g-Natural Metrics on the cotangent bundle. Int. Electron. J. Geom. 6(1), 129-146 (2013).
  2. Ağca, F. and Salimov, A. A.: Some notes concerning Cheeger-Gromoll metrics. Hacet. J. Math. Stat. 42(5), 533-549 (2013).
  3. Altunbas, M., Simsek, R., Gezer, A.: A Study Concerning Berger type deformed Sasaki Metric on the Tangent Bundle. Zh. Mat. Fiz. Anal.Geom. 15 (4), 435-447 (2019). https://doi.org/10.15407/mag15.04.435
  4. Cruceanu, V., Fortuny, P., Gadea, P. M.: A survey on paracomplex geometry. Rocky Mountain J. Math. 26 (1), 83-115 (1996). doi:10.1216/rmjm/1181072105
  5. Gezer, A., Altunbas, M.: On the Rescaled Riemannian Metric of Cheeger Gromoll Type on the Cotangent Bundle. Hacet. J. Math. Stat. 45 (2), 355-365 (2016). https:// Doi:10.15672/HJMS.20164515849
  6. Ells, J., Lemaire, L.: Another report on harmonic maps. Bull. London Math. Soc. 20 (5), 385-524 (1988). https://doi.org/10.1112/blms/20.5.385
  7. Eells, J., Sampson, J. H.: Harmonic mappings of Riemannian manifolds. Amer.J. Math. 86, 109-160 (1964). https://doi.org/10.2307/2373037
  8. Ocak, F. Notes About a New Metric on the Cotangent Bundle, Int. Electron. J. Geom. 12 (2), 241-249 (2019). https://doi.org/10.36890/iejg.542783
  9. Patterson, E. M., Walker, A. G.: Riemannian extensions. Quart. J.Math. Oxford Ser. 2(3), 19-28 (1952).
  10. Salimov, A. A., Agca, F.: Some Properties of Sasakian Metrics in Cotangent Bundles. Mediterr. J. Math. 8(2), 243-255 (2011). https://doi.org/10.1007/s00009-010-0080-x
  11. Salimov, A. A., Iscan, M., Etayo, F.: Para-holomorphic B-manifold and its properties. Topology Appl. 154(4), 925-933 (2007). https://doi.org/10.1016/j.topol.2006.10.003
  12. Sekizawa, M.: Natural transformations of affine connections on manifolds to metrics on cotangent bundles. In: Proceedings of 14thWinter School on Abstract Analysis (Srni, 1986), Rend. Circ. Mat. Palermo 14, 129-142 (1987).
  13. Yampolsky, A.: On geodesics of tangent bundle with fiberwise deformed Sasaki metric over Kahlerian manifolds. Zh. Mat. Fiz. Anal. Geom. 8 (2), 177-189 (2012).
  14. Yano, K., Ishihara, S.: Tangent and Cotangent Bundles, M. Dekker, New York, (1973).
  15. Zagane, A.: A new class of metrics on the cotangent bundle. Bull. Transilv. Univ. Brasov Ser. III 13(62)(1), 285-302 (2020). https://doi.org/10.31926/but.mif.2020.13.62.1.22). \url{ https://doi.org/10.1016/j.topol.2006.10.003}