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BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE

Yıl 2015, Cilt: 8 Sayı: 1, 45 - 52, 30.04.2015

Ayşe Yilmaz Ceylan Abdullah Aziz Ergin

https://doi.org/10.36890/iejg.592796

Öz


Anahtar Kelimeler

Cartan-Vranceanu space biharmonic curve Bertrand curve

Kaynakça

  • [1] Caddeo, R., Montaldo, S. and Oniciuc, C., Biharmonic submanifolds of S3., Internat. J.Math., 12(2002), no. 4, 867-876.
  • [2] Caddeo, R., Oniciuc, C. and Piu, P., Explicit formulas for non-geodesic biharmonic curves of the Heisenberg group, Rend. Sem. Mat. Univ. Politec, Torino, 62(2004), 265-278.
  • [3] Caddeo, R., Montaldo, S., Oniciuc, C. and Piu, P., The Classification of Biharmonic Curves of Cartan-Vranceanu 3-Dimensional Spaces, Modern trends in geometry and topology, Cluj Univ. Press, Cluj-Napoca, (2006), 121-131.
  • [4] Cho, J.T., Inoguchi J. and Lee, J., iharmonic curves in 3-dimensional Sasakian space forms, Annali di Matematica (2007). doi: 10.1007/s10231-006-0026-x
  • [5] Choi, J.H., Kang, T.H. and Kim, Y.H., Bertrand curves in 3- dimensional space forms, Appl. Math. Comput., 219(2012), 1040-1046.
  • [6] Dimitric, I., Submanifolds of Em with harmonic mean curvature vector, Modern trends in geometry and topology, Cluj Univ. Press, Cluj-Napoca, 20(1992), 53-65.
  • [7] Eells, J., Sampson, J.H., Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86(1964), 109-160.
  • [8] Fetcu, D., Biharmonic curves in the generalized Heisenberg Group, Contributions to Algebra and Geometry, 46(2005), no. 2, 513-521.
  • [9] Fetcu, D., Biharmonic curves in Cartan-Vranceanu (2n + 1)−Dimensional Spaces, Contribu- tions to Algebra and Geometry, 46(2007), no. 2, 513-521.
  • [10] Jiang, G.Y., 2−harmonic isometric immersions between Riemannian manifolds, Chinese Ann. Math., 7(1986), no. 2, 130-144.
  • [11] K¨orpınar, T. and Turhan, E., Characterization Bertrand Curve in the Heisenberg Group Heis3, Int. J. Open Problems Complex Analysis, 3(2011), no. 2, 61-67.
  • [12] Nutbourne, A.W. and Martin, R.R., Differential Geometry Applied to the Design of Curves and Surfaces, Ellis Horwood, Chichester, UK, 1988.

Yıl 2015, Cilt: 8 Sayı: 1, 45 - 52, 30.04.2015

Ayşe Yilmaz Ceylan Abdullah Aziz Ergin

https://doi.org/10.36890/iejg.592796

Öz

Kaynakça

  • [1] Caddeo, R., Montaldo, S. and Oniciuc, C., Biharmonic submanifolds of S3., Internat. J.Math., 12(2002), no. 4, 867-876.
  • [2] Caddeo, R., Oniciuc, C. and Piu, P., Explicit formulas for non-geodesic biharmonic curves of the Heisenberg group, Rend. Sem. Mat. Univ. Politec, Torino, 62(2004), 265-278.
  • [3] Caddeo, R., Montaldo, S., Oniciuc, C. and Piu, P., The Classification of Biharmonic Curves of Cartan-Vranceanu 3-Dimensional Spaces, Modern trends in geometry and topology, Cluj Univ. Press, Cluj-Napoca, (2006), 121-131.
  • [4] Cho, J.T., Inoguchi J. and Lee, J., iharmonic curves in 3-dimensional Sasakian space forms, Annali di Matematica (2007). doi: 10.1007/s10231-006-0026-x
  • [5] Choi, J.H., Kang, T.H. and Kim, Y.H., Bertrand curves in 3- dimensional space forms, Appl. Math. Comput., 219(2012), 1040-1046.
  • [6] Dimitric, I., Submanifolds of Em with harmonic mean curvature vector, Modern trends in geometry and topology, Cluj Univ. Press, Cluj-Napoca, 20(1992), 53-65.
  • [7] Eells, J., Sampson, J.H., Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86(1964), 109-160.
  • [8] Fetcu, D., Biharmonic curves in the generalized Heisenberg Group, Contributions to Algebra and Geometry, 46(2005), no. 2, 513-521.
  • [9] Fetcu, D., Biharmonic curves in Cartan-Vranceanu (2n + 1)−Dimensional Spaces, Contribu- tions to Algebra and Geometry, 46(2007), no. 2, 513-521.
  • [10] Jiang, G.Y., 2−harmonic isometric immersions between Riemannian manifolds, Chinese Ann. Math., 7(1986), no. 2, 130-144.
  • [11] K¨orpınar, T. and Turhan, E., Characterization Bertrand Curve in the Heisenberg Group Heis3, Int. J. Open Problems Complex Analysis, 3(2011), no. 2, 61-67.
  • [12] Nutbourne, A.W. and Martin, R.R., Differential Geometry Applied to the Design of Curves and Surfaces, Ellis Horwood, Chichester, UK, 1988.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Ayşe Yilmaz Ceylan Bu kişi benim

Abdullah Aziz Ergin Bu kişi benim

Yayımlanma Tarihi 30 Nisan 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 8 Sayı: 1

Kaynak Göster

APA Ceylan, A. Y., & Ergin, A. A. (2015). BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE. International Electronic Journal of Geometry, 8(1), 45-52. https://doi.org/10.36890/iejg.592796
AMA Ceylan AY, Ergin AA. BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE. Int. Electron. J. Geom. Nisan 2015;8(1):45-52. doi:10.36890/iejg.592796
Chicago Ceylan, Ayşe Yilmaz, ve Abdullah Aziz Ergin. “BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE”. International Electronic Journal of Geometry 8, sy. 1 (Nisan 2015): 45-52. https://doi.org/10.36890/iejg.592796.
EndNote Ceylan AY, Ergin AA (01 Nisan 2015) BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE. International Electronic Journal of Geometry 8 1 45–52.
IEEE A. Y. Ceylan ve A. A. Ergin, “BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE”, Int. Electron. J. Geom., c. 8, sy. 1, ss. 45–52, 2015, doi: 10.36890/iejg.592796.
ISNAD Ceylan, Ayşe Yilmaz - Ergin, Abdullah Aziz. “BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE”. International Electronic Journal of Geometry 8/1 (Nisan 2015), 45-52. https://doi.org/10.36890/iejg.592796.
JAMA Ceylan AY, Ergin AA. BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE. Int. Electron. J. Geom. 2015;8:45–52.
MLA Ceylan, Ayşe Yilmaz ve Abdullah Aziz Ergin. “BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE”. International Electronic Journal of Geometry, c. 8, sy. 1, 2015, ss. 45-52, doi:10.36890/iejg.592796.
Vancouver Ceylan AY, Ergin AA. BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE. Int. Electron. J. Geom. 2015;8(1):45-52.