Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2017, Cilt: 5 Sayı: 1, 85 - 92, 30.04.2017
https://doi.org/10.36753/mathenot.421709

Öz

Kaynakça

  • [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

Yıl 2017, Cilt: 5 Sayı: 1, 85 - 92, 30.04.2017
https://doi.org/10.36753/mathenot.421709

Öz

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

Kaynakça

  • [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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Abderrahim Zagane

Mustapha Djaa Bu kişi benim

Yayımlanma Tarihi 30 Nisan 2017
Gönderilme Tarihi 7 Mayıs 2016
Yayımlandığı Sayı Yıl 2017 Cilt: 5 Sayı: 1

Kaynak Göster

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. Nisan 2017;5(1):85-92. doi:10.36753/mathenot.421709
Chicago Zagane, Abderrahim, ve Mustapha Djaa. “On Geodesics of Warped Sasaki Metric”. Mathematical Sciences and Applications E-Notes 5, sy. 1 (Nisan 2017): 85-92. https://doi.org/10.36753/mathenot.421709.
EndNote Zagane A, Djaa M (01 Nisan 2017) On Geodesics of Warped Sasaki Metric. Mathematical Sciences and Applications E-Notes 5 1 85–92.
IEEE A. Zagane ve M. Djaa, “On Geodesics of Warped Sasaki Metric”, Math. Sci. Appl. E-Notes, c. 5, sy. 1, ss. 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 (Nisan 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 ve Mustapha Djaa. “On Geodesics of Warped Sasaki Metric”. Mathematical Sciences and Applications E-Notes, c. 5, sy. 1, 2017, ss. 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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