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Year 2018, Volume: 6 Issue: 1, 29 - 36, 27.04.2018

Fethi Latti Mustapha Djaa Abderrahim Zagane

https://doi.org/10.36753/mathenot.421753
Cited By: 5

Abstract

References

  • [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).
  • [4] 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.
  • [5] 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.
  • [7] 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).
  • [9] Eells, J. and Lemaire, L., Another report on harmonic maps, Bull. London Math. Soc. 20(1988), 385-524.
  • [10] Ishihara T., Harmonic sections of tangent bundles. J. Math. Tokushima Univ. 13 (1979), 23-27.
  • [11] Konderak J.J., On Harmonic Vector Fields, Publications Matematiques. Vol 36 (1992), 217-288.
  • [12] Opriou V., On Harmonic Maps Between Tangent Bundles. Rend. Sem. Mat, Vol 47, 1 (1989).
  • [13] Salimov, A., Gezer, A., Akbulut, K.: Geodesics of Sasakian metrics on tensor bundles. Mediterr. J. Math. 6, no.2, 135-147 (2009).
  • [14] 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.
  • [15] Salimov A. and Agca F. ,Some Properties of Sasakian Metrics in Cotangent Bundles. Mediterranean Journal of Mathematics; 8(2) (2011). 243-255.
  • [16] Salimov A. A. and Kazimova S., Geodesics of the Cheeger-Gromoll Metric, Turk J Math 33 (2009) , 99 - 105.
  • [17] Yano K., Ishihara S. Tangent and Cotangent Bundles, Marcel Dekker. INC. New York 1973.
  • [18] A. Zagane and M. Djaa, On geodesics of warped Sasaki metric, Mathematical sciences and Applications E-Notes. Vol1 (2017), 85-92.

Mus-Sasaki Metric and Harmonicity

Year 2018, Volume: 6 Issue: 1, 29 - 36, 27.04.2018

Fethi Latti Mustapha Djaa Abderrahim Zagane

https://doi.org/10.36753/mathenot.421753
Cited By: 5

Abstract

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

Keywords

Horizontal lift vertical lift Mus-Sasaki metric harmonic vector field

References

  • [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).
  • [4] 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.
  • [5] 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.
  • [7] 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).
  • [9] Eells, J. and Lemaire, L., Another report on harmonic maps, Bull. London Math. Soc. 20(1988), 385-524.
  • [10] Ishihara T., Harmonic sections of tangent bundles. J. Math. Tokushima Univ. 13 (1979), 23-27.
  • [11] Konderak J.J., On Harmonic Vector Fields, Publications Matematiques. Vol 36 (1992), 217-288.
  • [12] Opriou V., On Harmonic Maps Between Tangent Bundles. Rend. Sem. Mat, Vol 47, 1 (1989).
  • [13] Salimov, A., Gezer, A., Akbulut, K.: Geodesics of Sasakian metrics on tensor bundles. Mediterr. J. Math. 6, no.2, 135-147 (2009).
  • [14] 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.
  • [15] Salimov A. and Agca F. ,Some Properties of Sasakian Metrics in Cotangent Bundles. Mediterranean Journal of Mathematics; 8(2) (2011). 243-255.
  • [16] Salimov A. A. and Kazimova S., Geodesics of the Cheeger-Gromoll Metric, Turk J Math 33 (2009) , 99 - 105.
  • [17] Yano K., Ishihara S. Tangent and Cotangent Bundles, Marcel Dekker. INC. New York 1973.
  • [18] A. Zagane and M. Djaa, On geodesics of warped Sasaki metric, Mathematical sciences and Applications E-Notes. Vol1 (2017), 85-92.
There are 18 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Fethi Latti This is me

Mustapha Djaa This is me

Abderrahim Zagane

Publication Date April 27, 2018
Submission Date May 17, 2017
Published in Issue Year 2018 Volume: 6 Issue: 1

Cite

APA Latti, F., Djaa, M., & Zagane, A. (2018). Mus-Sasaki Metric and Harmonicity. Mathematical Sciences and Applications E-Notes, 6(1), 29-36. https://doi.org/10.36753/mathenot.421753
AMA Latti F, Djaa M, Zagane A. Mus-Sasaki Metric and Harmonicity. Math. Sci. Appl. E-Notes. April 2018;6(1):29-36. doi:10.36753/mathenot.421753
Chicago Latti, Fethi, Mustapha Djaa, and Abderrahim Zagane. “Mus-Sasaki Metric and Harmonicity”. Mathematical Sciences and Applications E-Notes 6, no. 1 (April 2018): 29-36. https://doi.org/10.36753/mathenot.421753.
EndNote Latti F, Djaa M, Zagane A (April 1, 2018) Mus-Sasaki Metric and Harmonicity. Mathematical Sciences and Applications E-Notes 6 1 29–36.
IEEE F. Latti, M. Djaa, and A. Zagane, “Mus-Sasaki Metric and Harmonicity”, Math. Sci. Appl. E-Notes, vol. 6, no. 1, pp. 29–36, 2018, doi: 10.36753/mathenot.421753.
ISNAD Latti, Fethi et al. “Mus-Sasaki Metric and Harmonicity”. Mathematical Sciences and Applications E-Notes 6/1 (April 2018), 29-36. https://doi.org/10.36753/mathenot.421753.
JAMA Latti F, Djaa M, Zagane A. Mus-Sasaki Metric and Harmonicity. Math. Sci. Appl. E-Notes. 2018;6:29–36.
MLA Latti, Fethi et al. “Mus-Sasaki Metric and Harmonicity”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 1, 2018, pp. 29-36, doi:10.36753/mathenot.421753.
Vancouver Latti F, Djaa M, Zagane A. Mus-Sasaki Metric and Harmonicity. Math. Sci. Appl. E-Notes. 2018;6(1):29-36.

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