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Year 2017, Volume: 5 Issue: 1, 85 - 92, 30.04.2017

Abderrahim Zagane Mustapha Djaa

https://doi.org/10.36753/mathenot.421709
Cited By: 7

Abstract

References

  • [1] Cengiz, N., Salimov, A.A., Diagonal lift in the tensor bundle and its applications. Appl. Math. Comput. 142, no. 2-3, 309-319 (2003).
  • [2] Cherif, A.M., and Djaa, M., Geometry of energy and bienergy variations between Riemannian manifolds, Kyungpook Mathematical Journal, 55(2015), pp 715-730.
  • [3] 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.
  • [4] Djaa M., Gancarzewicz J., The geometry of tangent bundles of order r, Boletin Academia , Galega de Ciencias ,Espagne, 4 (1985), 147–165.
  • [5] Djaa, M., Djaa, N.E.H. and R. Nasri, Natural Metrics on T2M and Harmonicity, International Electronic Journal of Geometry Volume 6 No.1(2013), 100-111.
  • [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), 283-298.
  • [8] Djaa, N.E.H. and Djaa, M., Generalized Warped Product Manifold and Critical Riemannian Metric, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis Vol 28 (2012), 197-206.
  • [9] Elhendi, H., Terbeche, M. And Djaa, M., Tangent Bundle Of Order Two And Biharmonicity. Acta Math. Univ. Comenianae . Vol. 83 2 (2014). pp. 165-179.
  • [10] GEZER, A., On the tangent bundle with deformed Sasaki metric, Int. Electron. J. Geom. Volume 6 No. 2 (2013), 19-31.
  • [11] Gudmundsson, S. and Kappos, E.: On the Geometry of the Tangent Bundles, Expo. Math. 20, no.1(2002), 1-41.
  • [12] Salimov, A., Gezer, A., Akbulut, K., Geodesics of Sasakian metrics on tensor bundles. Mediterr. J. Math. 6, no.2, 135-147 (2009).
  • [13] 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.
  • [14] Salimov A. and Agca F. ,Some Properties of Sasakian Metrics in Cotangent Bundles. Mediterranean Journal of Mathematics; 8(2) (2011). 243-255.
  • [15] Salimov A. A. and Kazimova S., Geodesics of the Cheeger-Gromoll Metric, Turk J Math 33 (2009) , 99 - 105.
  • [16] Yano K., Ishihara S. Tangent and Cotangent Bundles, Marcel Dekker. INC. New York 1973.

On Geodesics of Warped Sasaki Metric

Year 2017, Volume: 5 Issue: 1, 85 - 92, 30.04.2017

Abderrahim Zagane Mustapha Djaa

https://doi.org/10.36753/mathenot.421709
Cited By: 7

Abstract

In this paper we establish a necessary and sufficient conditions under which a curve be a geodesic respect
to the warped Sasaki metric.

Keywords

Horizontal lift vertical lift warped Sasaki metric geodesic

References

  • [1] Cengiz, N., Salimov, A.A., Diagonal lift in the tensor bundle and its applications. Appl. Math. Comput. 142, no. 2-3, 309-319 (2003).
  • [2] Cherif, A.M., and Djaa, M., Geometry of energy and bienergy variations between Riemannian manifolds, Kyungpook Mathematical Journal, 55(2015), pp 715-730.
  • [3] 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.
  • [4] Djaa M., Gancarzewicz J., The geometry of tangent bundles of order r, Boletin Academia , Galega de Ciencias ,Espagne, 4 (1985), 147–165.
  • [5] Djaa, M., Djaa, N.E.H. and R. Nasri, Natural Metrics on T2M and Harmonicity, International Electronic Journal of Geometry Volume 6 No.1(2013), 100-111.
  • [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), 283-298.
  • [8] Djaa, N.E.H. and Djaa, M., Generalized Warped Product Manifold and Critical Riemannian Metric, Acta Mathematica Academiae Paedagogicae Nyiregyhaziensis Vol 28 (2012), 197-206.
  • [9] Elhendi, H., Terbeche, M. And Djaa, M., Tangent Bundle Of Order Two And Biharmonicity. Acta Math. Univ. Comenianae . Vol. 83 2 (2014). pp. 165-179.
  • [10] GEZER, A., On the tangent bundle with deformed Sasaki metric, Int. Electron. J. Geom. Volume 6 No. 2 (2013), 19-31.
  • [11] Gudmundsson, S. and Kappos, E.: On the Geometry of the Tangent Bundles, Expo. Math. 20, no.1(2002), 1-41.
  • [12] Salimov, A., Gezer, A., Akbulut, K., Geodesics of Sasakian metrics on tensor bundles. Mediterr. J. Math. 6, no.2, 135-147 (2009).
  • [13] 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.
  • [14] Salimov A. and Agca F. ,Some Properties of Sasakian Metrics in Cotangent Bundles. Mediterranean Journal of Mathematics; 8(2) (2011). 243-255.
  • [15] Salimov A. A. and Kazimova S., Geodesics of the Cheeger-Gromoll Metric, Turk J Math 33 (2009) , 99 - 105.
  • [16] Yano K., Ishihara S. Tangent and Cotangent Bundles, Marcel Dekker. INC. New York 1973.
There are 16 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Abderrahim Zagane

Mustapha Djaa This is me

Publication Date April 30, 2017
Submission Date May 7, 2016
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Zagane, A., & Djaa, M. (2017). On Geodesics of Warped Sasaki Metric. Mathematical Sciences and Applications E-Notes, 5(1), 85-92. https://doi.org/10.36753/mathenot.421709
AMA Zagane A, Djaa M. On Geodesics of Warped Sasaki Metric. Math. Sci. Appl. E-Notes. April 2017;5(1):85-92. doi:10.36753/mathenot.421709
Chicago Zagane, Abderrahim, and Mustapha Djaa. “On Geodesics of Warped Sasaki Metric”. Mathematical Sciences and Applications E-Notes 5, no. 1 (April 2017): 85-92. https://doi.org/10.36753/mathenot.421709.
EndNote Zagane A, Djaa M (April 1, 2017) On Geodesics of Warped Sasaki Metric. Mathematical Sciences and Applications E-Notes 5 1 85–92.
IEEE A. Zagane and M. Djaa, “On Geodesics of Warped Sasaki Metric”, Math. Sci. Appl. E-Notes, vol. 5, no. 1, pp. 85–92, 2017, doi: 10.36753/mathenot.421709.
ISNAD Zagane, Abderrahim - Djaa, Mustapha. “On Geodesics of Warped Sasaki Metric”. Mathematical Sciences and Applications E-Notes 5/1 (April 2017), 85-92. https://doi.org/10.36753/mathenot.421709.
JAMA Zagane A, Djaa M. On Geodesics of Warped Sasaki Metric. Math. Sci. Appl. E-Notes. 2017;5:85–92.
MLA Zagane, Abderrahim and Mustapha Djaa. “On Geodesics of Warped Sasaki Metric”. Mathematical Sciences and Applications E-Notes, vol. 5, no. 1, 2017, pp. 85-92, doi:10.36753/mathenot.421709.
Vancouver Zagane A, Djaa M. On Geodesics of Warped Sasaki Metric. Math. Sci. Appl. E-Notes. 2017;5(1):85-92.

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