Research Article

Darboux Frame of a Curve Lying on a Lightlike Surface

Volume: 4 Number: 2 October 30, 2016
E. Selcen Yakıcı Topbaş , İsmail Gök , Nejat Ekmekci , Yusuf Yaylı
EN

Darboux Frame of a Curve Lying on a Lightlike Surface

Abstract

In this study, the Darboux frame is given for a curve lying on the lightlike surface of three dimensional Minkowski space. Moreover, known curvatures of the curve are obtained according to the Darboux frame and relationships between these curvatures are acquired. In specific case, by taking into consideration that the surface is a lightlike cone, similar characterizations are investigated.

Keywords

Darboux frame,Lightlike surface,Lightlike cone,Helix

References

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  2. [2] Duggal, K., L., Sahin, B., Differential Geometry of Lightlike Submanifolds, Birkhauser Verlag AG, Germany, (2010).
  3. [3] Liu, H., Curves in the lightlike cone, Contributions to Algebra and Geometry, 45 (2004), No. 1, pp. 291-303.
  4. [4] Liu, H., and Meng, Q., Representation Formulas of Curves in a Two- and Three-Dimensional Lightlike Cone, 59 (2011), pp. 437-451.
  5. [5] Lopez, R., Diferential Geometry of Curves and Surfaces in Lorentz-Minkowski space, Mini-Course taught at the Instituto de Mathematica e Estatistica (IME-USP) University of Sao Paulo, Brasil (2008).
  6. [6] O’Neill, B., Semi-Riemannian Geometry, Academic Press, NewYork 1983. .Zbl 0531.53051 (1983).
  7. [7] Sabuncuo ˘glu, A., Diferensiyel Geometri, Nobel Yayıncılık, Ankara. (2011).
APA
Topbaş, E. S. Y., Gök, İ., Ekmekci, N., & Yaylı, Y. (2016). Darboux Frame of a Curve Lying on a Lightlike Surface. Mathematical Sciences and Applications E-Notes, 4(2), 121-130. https://doi.org/10.36753/mathenot.421465
AMA
1.Topbaş ESY, Gök İ, Ekmekci N, Yaylı Y. Darboux Frame of a Curve Lying on a Lightlike Surface. Math. Sci. Appl. E-Notes. 2016;4(2):121-130. doi:10.36753/mathenot.421465
Chicago
Topbaş, E. Selcen Yakıcı, İsmail Gök, Nejat Ekmekci, and Yusuf Yaylı. 2016. “Darboux Frame of a Curve Lying on a Lightlike Surface”. Mathematical Sciences and Applications E-Notes 4 (2): 121-30. https://doi.org/10.36753/mathenot.421465.
EndNote
Topbaş ESY, Gök İ, Ekmekci N, Yaylı Y (October 1, 2016) Darboux Frame of a Curve Lying on a Lightlike Surface. Mathematical Sciences and Applications E-Notes 4 2 121–130.
IEEE
[1]E. S. Y. Topbaş, İ. Gök, N. Ekmekci, and Y. Yaylı, “Darboux Frame of a Curve Lying on a Lightlike Surface”, Math. Sci. Appl. E-Notes, vol. 4, no. 2, pp. 121–130, Oct. 2016, doi: 10.36753/mathenot.421465.
ISNAD
Topbaş, E. Selcen Yakıcı - Gök, İsmail - Ekmekci, Nejat - Yaylı, Yusuf. “Darboux Frame of a Curve Lying on a Lightlike Surface”. Mathematical Sciences and Applications E-Notes 4/2 (October 1, 2016): 121-130. https://doi.org/10.36753/mathenot.421465.
JAMA
1.Topbaş ESY, Gök İ, Ekmekci N, Yaylı Y. Darboux Frame of a Curve Lying on a Lightlike Surface. Math. Sci. Appl. E-Notes. 2016;4:121–130.
MLA
Topbaş, E. Selcen Yakıcı, et al. “Darboux Frame of a Curve Lying on a Lightlike Surface”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 2, Oct. 2016, pp. 121-30, doi:10.36753/mathenot.421465.
Vancouver
1.E. Selcen Yakıcı Topbaş, İsmail Gök, Nejat Ekmekci, Yusuf Yaylı. Darboux Frame of a Curve Lying on a Lightlike Surface. Math. Sci. Appl. E-Notes. 2016 Oct. 1;4(2):121-30. doi:10.36753/mathenot.421465