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Journals / Mathematical Sciences and Applications E-Notes / 2018 / Cilt: 6 - Sayı: 1

Mus-Sasaki Metric and Harmonicity

Mustapha DJAA
Fethi LATTI
Abderrahim ZAGANE
Pages
29–36
Publication Date
2022-10-19
DOI
—
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AI Summary & Key Takeaways

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

We also construct some examples of harmonic vector fields.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce the Mus-Sasaki metric on the tangent bundle TM, as a new natural metric onTM.
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Key Findings & Data:We establish necessary and sufficient conditions under which a vector field is harmonic with respectto the Mus-Sasaki metric.
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Conclusion & Impact:We also construct some examples of harmonic vector fields.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we introduce the Mus-Sasaki metric on the tangent bundle TM, as a new natural metric onTM. We establish necessary and sufficient conditions under which a vector field is harmonic with respectto the Mus-Sasaki metric. We also construct some examples of harmonic vector fields.

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Cite This Article

DJAA, M., LATTI, F., ZAGANE, A. (2022). Mus-Sasaki Metric and Harmonicity. Mathematical Sciences and Applications E-Notes, Cilt: 6 - Sayı: 1, 29–36. https://ajindex.com/articles/578869

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References (15)

  1. Boeckx E. and Vanhecke L., Harmonic and minimal vector fields on tangent and unit tangent bundles, Differential Geometry and its Applications Volume 13, Issue 1, July 2000, Pages 77-93
  2. Calvaruso G., Naturally Harmonic Vector Fields, Note di Matematica, Note Mat. 1(2008), suppl. n. 1, 107-130 [3] Cengiz, N., Salimov, A.A.: Diagonal lift in the tensor bundle and its applications. Appl. Math. Comput. 142, no. 2-3, 309-319 (2003)
  3. Djaa M., Mohamed Cherif A., Zegga K. And Ouakkas S., On the Generalized of Harmonic and Bi-harmonic Maps, international electronic journal ofgeometry, 5 no. 1(2012), 90-100
  4. Djaa M., Gancarzewicz J., The geometry of tangent bundles of order r, Boletin Academia, Galega de Ciencias,Espagne, 4 (1985), 147–165 [6] Djaa N.E.H., Ouakkas S., M. Djaa, Harmonic sections on the tangent bundle of order two. Annales Mathematicae et Informaticae 38( 2011) pp 15-25. 1
  5. Djaa N.E.H., Boulal A. and Zagane A., Generalized warped product manifolds and Biharmonic maps, Acta Math. Univ. Comenianae Vol. LXXXI, 2 (2012), pp. 283-298 [8] Eells J., Sampson J.H., Harmonic mappings of Riemannian manifolds. Amer. J. Maths. 86(1964)
  6. Eells, J. and Lemaire, L., Another report on harmonic maps, Bull. London Math. Soc. 20(1988), 385-524
  7. Ishihara T., Harmonic sections of tangent bundles. J. Math. Tokushima Univ. 13 (1979), 23-27
  8. Konderak J.J., On Harmonic Vector Fields, Publications Matematiques. Vol 36 (1992), 217-288
  9. Opriou V., On Harmonic Maps Between Tangent Bundles. Rend. Sem. Mat, Vol 47, 1 (1989)
  10. Salimov, A., Gezer, A., Akbulut, K.: Geodesics of Sasakian metrics on tensor bundles. Mediterr. J. Math. 6, no.2, 135-147 (2009)
  11. Salimov, A., Gezer, A., On the geometry of the (1, 1)-tensor bundle with Sasaki type metric. Chinese Annals of Mathematics, Series B May 2011, Volume 32, Issue 3, pp 369-386
  12. Salimov A. and Agca F.,Some Properties of Sasakian Metrics in Cotangent Bundles. Mediterranean Journal of Mathematics; 8(2) (2011). 243-255
  13. Salimov A. A. and Kazimova S., Geodesics of the Cheeger-Gromoll Metric, Turk J Math 33 (2009), 99 - 105
  14. Yano K., Ishihara S. Tangent and Cotangent Bundles, Marcel Dekker. INC. New York 1973
  15. A. Zagane and M. Djaa, On geodesics of warped Sasaki metric, Mathematical sciences and Applications E-Notes. Vol1 (2017), 85-92.