Research Article

Spherical indicatrices of a Bertrand curve in three dimensional Lie groups

Volume: 68 Number: 2 August 1, 2019
EN

Spherical indicatrices of a Bertrand curve in three dimensional Lie groups

Abstract

In this paper, new representations of a Bertrand curve pair in three dimensional Lie groups with bi-invariant metric are given. Besides, the spherical indicatrices of a Bertrand curve pair are obtained and the relations between the spherical indicatrices and new representations of Bertrand curve pair are shown.

Keywords

References

  1. Ahmat, T. A., New special curves and their spherical indicatrices,Global Journal of Advanced Research on Classical and Modern Geometries, 1 (2), (2012), 28-38.
  2. Cöken, A. C. and Çiftçi, Ü., A note on the geometry of Lie groups, Nonlinear Analysis, TMA68 (2008), 2013-2016.
  3. Crouch, P. and Leite, F. S., The dynamic interpolation problem: on Riemannian manifolds, Lie groups and symmetric spaces, J. Dyn. Control Syst. 1(2), (1995), 177-202.
  4. Çiftçi, Ü., A generalization of Lancert's theorem, J. Geom. Phys. 59 (2009), 1597-1603.
  5. Do Espırito-Santo, N., Fornari, S., Frensel, K. and Ripoll, J., Constant mean curvature hypersurfaces in a Lie group with a bi-invariant metric, Manuscripta Math. 111 (4), (2003), 459-470.
  6. Ekmekci, N. and İlarslan, K., On Bertrand curves and their characterization, Differ. Geom.Dyn.Syst. 3 (2001), no. 2, 17-24.
  7. Gök, İ., Okuyucu, O. Z., Ekmekci, N. and Yaylı, Y., On Mannheim partner curves in three dimensional Lie groups, Miskolc Mathematical Notes, 17(2), (2017), 999-1010.
  8. Izumiya, S. and Takeuchi, N., Generic properties of helices and Bertrand curves, J. Geom. 74 (2002), 97--109.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

August 1, 2019

Submission Date

March 29, 2018

Acceptance Date

March 12, 2019

Published in Issue

Year 2019 Volume: 68 Number: 2

APA
Çakmak, A., & Kızıltuğ, S. (2019). Spherical indicatrices of a Bertrand curve in three dimensional Lie groups. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1930-1938. https://doi.org/10.31801/cfsuasmas.571964
AMA
1.Çakmak A, Kızıltuğ S. Spherical indicatrices of a Bertrand curve in three dimensional Lie groups. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1930-1938. doi:10.31801/cfsuasmas.571964
Chicago
Çakmak, Ali, and Sezai Kızıltuğ. 2019. “Spherical Indicatrices of a Bertrand Curve in Three Dimensional Lie Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 (2): 1930-38. https://doi.org/10.31801/cfsuasmas.571964.
EndNote
Çakmak A, Kızıltuğ S (August 1, 2019) Spherical indicatrices of a Bertrand curve in three dimensional Lie groups. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1930–1938.
IEEE
[1]A. Çakmak and S. Kızıltuğ, “Spherical indicatrices of a Bertrand curve in three dimensional Lie groups”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1930–1938, Aug. 2019, doi: 10.31801/cfsuasmas.571964.
ISNAD
Çakmak, Ali - Kızıltuğ, Sezai. “Spherical Indicatrices of a Bertrand Curve in Three Dimensional Lie Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 1, 2019): 1930-1938. https://doi.org/10.31801/cfsuasmas.571964.
JAMA
1.Çakmak A, Kızıltuğ S. Spherical indicatrices of a Bertrand curve in three dimensional Lie groups. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1930–1938.
MLA
Çakmak, Ali, and Sezai Kızıltuğ. “Spherical Indicatrices of a Bertrand Curve in Three Dimensional Lie Groups”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, Aug. 2019, pp. 1930-8, doi:10.31801/cfsuasmas.571964.
Vancouver
1.Ali Çakmak, Sezai Kızıltuğ. Spherical indicatrices of a Bertrand curve in three dimensional Lie groups. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019 Aug. 1;68(2):1930-8. doi:10.31801/cfsuasmas.571964

Cited By

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

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