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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 69 Issue: 1

On generalized Cheeger-Gromoll metric and harmonicity

Abderrahim Zagane(Relizane Univesity)0000-0001-9339-3787
Mustapha Djaa(Relizane University)0000-0002-7330-2144
Reda Kada Ben Otmane(Mascara University)0000-0002-0185-6324
Sayfa
—
Yayın Tarihi
2020-06-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We also construct some examples of harmonic vector fields.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we introduce the Generalized Cheeger-Gromoll metric on the tangent bundle TM, as a natural metric on TM.
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Temel Bulgular & Veri:We establish a necessary and sufficient conditions under which a vector field is harmonic with respect to the Generalized Cheeger-Gromoll metric.
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Sonuç & Katkı:We also construct some examples of harmonic vector fields.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Horizontal lift · vertical lift · generalized Cheeger-Gromoll metric

Abstract

In this paper, we introduce the Generalized Cheeger-Gromoll metric on the tangent bundle TM, as a natural metric on TM. We establish a necessary and sufficient conditions under which a vector field is harmonic with respect to the Generalized Cheeger-Gromoll metric. We also construct some examples of harmonic vector fields.

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Bu Makaleye Atıf Yap

Zagane, A., Djaa, M., Otmane, R. K. B. (2020). On generalized Cheeger-Gromoll metric and harmonicity. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 69 Issue: 1. https://doi.org/10.31801/cfsuasmas.487296

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Kaynakça (30)

  1. Abbassi, M.T.K. and Sarih, M., On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math., 41 (2005), 71-92.
  2. Anastasiei, M., Locally conformal Kaehler structures on tangent bundle of a space form, Libertas Math., 19 (1999), 71-76.
  3. Boeckx, E. and Vanhecke, L., Harmonic and minimal vector fields on unit tangent bundles, Differential Geometry and Applications, Volume 13, Issue 1, July 2000, Pages 77-93.
  4. Calvaruso, G., Naturally Harmonic Vector Fields, Note di Matematica, Note Mat., suppl.n.1, 1 (2008), 107-130.
  5. Cheeger, J. and Gromoll, D., On the structure of complete manifolds of nonnegative curvature, Ann. of Math., (2) 96 (1972), 413-443.
  6. Cengiz, N., Salimov, A.A., Diagonal lift in the tensor bundle and its applications. Appl. Math. Comput. 142, no.2-3 (2003), 309-319.
  7. Cherif, A.M. and Djaa, M., On the Biharmonic maps with potential, Arab Journal Mathemaical Sciences, AJMS Elsevier, 24(1) (2018), 1-8.
  8. Djaa, M. and Cherif, A. M., On Generalized f-biharmonic Maps and Stress f-bienergy Tensor, Journal of Geometry and Symmetry in Physics JGSP, 29 (2013), pp. 65-81.
  9. Djaa, M., Mohamed Cherif, A., Zegga, K. And Ouakkas, S., On the Generalized of harmonic and Bi-harmonic Maps, International electronic journal of geometry, 5 no. 1 (2012), 90-100.
  10. Djaa, M. and Gancarzewicz, J., The geometry of tangent bundles of order r, Boletin Academia, Galega de Ciencias, Espagne, 4 (1985), 147-165
  11. Djaa, N.E.H., Ouakkas, S. and Djaa, M., Harmonic sections on the tangent bundle of order two, Annales Mathematicae et Informaticae, 38 (2011), 15-25.
  12. Djaa, N.E.H., Boulal, A. and Zagane, A., Generalized warped product manifolds and Biharmonic maps, Acta Math. Univ. Comenianae, Vol. LXXXI, 2 (2012), 283-298.
  13. Dombrowski, P., On the geometry of tangent bundle, J. Reine Angew.Math., 210 (1962), 73-88.
  14. Ells, J. and Sampson, J.H., Harmonic mappings of Riemannian manifolds. Amer.J. Maths., 86 (1964).
  15. Ells, J. and Lemaire, L., Another report on harmonic maps, Bull. London Math. Soc., 20 (1988), 385-524.
  16. Gezer, A. and Altunbas, M., Some notes concerning Riemannian metrics of Cheeger-Gromoll type, J. Math. Anal. Appl., 396 (2012) 119-132.
  17. Gudmunsson, S. and Kappos, E., On the Geometry of Tangent Bundles, Expo.Math., 20 (2002),1-41.
  18. Ishihara, T., Harmonic sections of tangent bundles, J. Math. Tokushima Univ., 13 1979), 23-27.
  19. Konderak, J.J., On Harmonic Vector Fields, Publications Mathematiques, Vol 36, (1992), 217-288.
  20. Latti, F., Djaa, M. and Zagane, A., Mus-Sasaki Metric and Harmonicity, Mathematical Sciences and Applications E-Notes, 6 (1) (2018), 29-36.
  21. Munteanu, M., Some Aspects on the Geometry of the Tangent Bundles and Tangent Sphere Bundles of Riemannian Manifold, Mediterr. J. Math., 5 (2008), 43-59.
  22. Opriou, V., On Harmonic Maps Between tangent bundles, Rend. Sem.Mat., Vol 47, 1(1989).
  23. Salimov, A. A., Gezer, A. and Akbulut, K., Geodesics of Sasakian metrics on tensor bundles, Mediterr. J. Math., 6, no.2 (2009), 135-147.
  24. Salimov, A. A. and Kazimova, S., Geodesics of the Cheeger-Gromoll Metric, Turk J Math., 33 (2009), 99 - 105.
  25. Sasaki, S., On the differential geometry of tangent bundles of Riemannian manifolds, Tohoku Math. J., 10 (1958), 338-354.
  26. Sekizawa, M., Curvatures of Tangent Bundles with Cheeger-Gromoll Metric, Tokyo J. Math., 14, No. 2 (1991), 407-417.
  27. Yano, K. and Ishihara, S., Tangent and Cotangent Bundles, Marcel Dekker INC. New York, 1-171, 1973.
  28. Zagane, A. and Djaa, M., On Geodesics of Warped Sasaki Metric, Mathematical Sciences and Applications E-Notes 5 (1) (2017), 85-92.
  29. Djaa, M. and Gancarzewicz, J., The geometry of tangent bundles of order r, Boletin Academia, Galega de Ciencias, Espagne, 4 (1985), 147-165
  30. Dombrowski, P., On the geometry of tangent bundle, J. Reine Angew.Math., 210 (1962), 73-88.