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

Year 2015, , 45 - 52, 30.04.2015

Ayşe Yilmaz Ceylan Abdullah Aziz Ergin

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

Abstract


Keywords

Cartan-Vranceanu space biharmonic curve Bertrand curve

References

  • [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.

Year 2015, , 45 - 52, 30.04.2015

Ayşe Yilmaz Ceylan Abdullah Aziz Ergin

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

Abstract

References

  • [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.
There are 12 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Ayşe Yilmaz Ceylan This is me

Abdullah Aziz Ergin This is me

Publication Date April 30, 2015
Published in Issue Year 2015

Cite

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. April 2015;8(1):45-52. doi:10.36890/iejg.592796
Chicago Ceylan, Ayşe Yilmaz, and Abdullah Aziz Ergin. “BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE”. International Electronic Journal of Geometry 8, no. 1 (April 2015): 45-52. https://doi.org/10.36890/iejg.592796.
EndNote Ceylan AY, Ergin AA (April 1, 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 and A. A. Ergin, “BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE”, Int. Electron. J. Geom., vol. 8, no. 1, pp. 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 (April 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 and Abdullah Aziz Ergin. “BERTRAND MATE OF A BIHARMONIC CURVE IN CARTAN-VRANCEANU 3-DIMENSIONAL SPACE”. International Electronic Journal of Geometry, vol. 8, no. 1, 2015, pp. 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.