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

Ayşe Yilmaz Ceylan; Abdullah Aziz Ergin

doi:10.36890/iejg.592796

Research Article

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

Year 2015, Volume: 8 Issue: 1, 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, Volume: 8 Issue: 1, 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 Volume: 8 Issue: 1

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.