On Geodesics of Warped Sasaki Metric

Abderrahim Zagane; Mustapha Djaa

doi:10.36753/mathenot.421709

EN

On Geodesics of Warped Sasaki Metric

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.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Abderrahim Zagane

Mustapha Djaa This is me

Publication Date

April 30, 2017

Submission Date

May 7, 2016

Acceptance Date

-

Published in Issue

Year 2017 Volume: 5 Number: 1

DOI

https://doi.org/10.36753/mathenot.421709

IZ

https://izlik.org/JA46TA55FF

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

1.Zagane A, Djaa M. On Geodesics of Warped Sasaki Metric. Math. Sci. Appl. E-Notes. 2017;5(1):85-92. doi:10.36753/mathenot.421709

Chicago

Zagane, Abderrahim, and Mustapha Djaa. 2017. “On Geodesics of Warped Sasaki Metric”. Mathematical Sciences and Applications E-Notes 5 (1): 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

[1]A. Zagane and M. Djaa, “On Geodesics of Warped Sasaki Metric”, Math. Sci. Appl. E-Notes, vol. 5, no. 1, pp. 85–92, Apr. 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 1, 2017): 85-92. https://doi.org/10.36753/mathenot.421709.

JAMA

1.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, Apr. 2017, pp. 85-92, doi:10.36753/mathenot.421709.

Vancouver

1.Abderrahim Zagane, Mustapha Djaa. On Geodesics of Warped Sasaki Metric. Math. Sci. Appl. E-Notes. 2017 Apr. 1;5(1):85-92. doi:10.36753/mathenot.421709

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On Geodesics of Warped Sasaki Metric

Abstract

On Geodesics of Warped Sasaki Metric

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite

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