surfaces according to Sabban frame in the Heisenberg group Heis . We characterize the biharmonic curves in terms of their geodesic curvature and we prove that all of biharmonic curves are helices in the Heisenberg group Heis . Finally, we find explicit parametric equations of  surfaces according to Sabban Frame.

">

S-α Surfaces Of Biharmonic S-Curves According To Sabban Frame In Heisenberg Group Heis3

Talat Körpinar*, Essin TURHAN**
*-** Firat University, Department of Mathematics, Elazig, Turkey.
Periodicity:April - June'2012
DOI : https://doi.org/10.26634/jmat.1.2.1844

Abstract

In this paper, we study  surfaces according to Sabban frame in the Heisenberg group Heis . We characterize the biharmonic curves in terms of their geodesic curvature and we prove that all of biharmonic curves are helices in the Heisenberg group Heis . Finally, we find explicit parametric equations of  surfaces according to Sabban Frame.

Keywords

Biharmonic curve, Heisenberg group, Sabban frame.

How to Cite this Article?

Körpinar, T., and Turhan, E. (2012). S-? Surfaces Of Biharmonic S-Curves According To Sabban Frame In Heisenberg Group Heis3. i-manager’s Journal on Mathematics, 1(2), 1-6. https://doi.org/10.26634/jmat.1.2.1844

References

[1]. M. Babaarslan and Y. Yayli: The characterizations of constant slope surfaces and Bertrand curves, International Journal of the Physical Sciences 6(8) (2011), 1868-1875.
[2]. R. Caddeo and S. Montaldo: Biharmonic submanifolds of S , Internat. J. Math. 12(8) (2001), 867--876.
[3]. B. Y. Chen: Some open problems and conjectures on submanifolds of finite type, Soochow J. Math. 17 (1991), 169--188.
[4]. I. Dimitric: Submanifolds of Em with harmonic mean curvature vector, Bull. Inst. Math. Acad. Sinica 20 (1992), 53--65.
[5]. J. Eells and L. Lemaire: A report on harmonic maps, Bull. London Math. Soc. 10 (1978), 1--68.
[6]. J. Eells and J. H. Sampson: Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109--160.
[7]. S. Izumiya and N. Takeuchi: Special Curves and Ruled Surfaces, Contributions to Algebra and Geometry 44 (2003), 203- 212.
[8]. G. Y. Jiang: 2-harmonic maps and their first and second variational formulas, Chinese Ann. Math. Ser. A 7(4) (1986), 389-- 402.
[9]. T. Körpinar, E. Turhan: Biharmonic S-Curves According to Sabban Frame in Heisenberg Group Heis , Bol. Soc. Paran. Mat. 31 (1) (2013), 205-211.
[10]. E. Loubeau and S. Montaldo: Biminimal immersions in space forms, preprint, 2004, math.DG/0405320 v1.
[11]. B. O'Neill: Semi-Riemannian Geometry, Academic Press, New York (1983).
[12]. E. Turhan, T. Körpinar: On Characterization Of Timelike Horizontal Biharmonic Curves In The Lorentzian Heisenberg Group Heis , Zeitschrift für Naturforschung A- A Journal of Physical Sciences 65a (2010), 641-648.
[13]. E. Turhan, T. Körpinar: On Characterization Canal Surfaces around Timelike Horizontal Biharmonic Curves in Lorentzian Heisenberg Group Heis , Zeitschrift für Naturforschung A- A Journal of Physical Sciences 66a (2011), 441-449.
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.