Research Article
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Year 2016, , 121 - 130, 30.10.2016
https://doi.org/10.36753/mathenot.421465

Abstract

References

  • [1] Duggal, K., L., Bejancu, A., Lightlikesubmanifolds of Semi-Riemannian Manifolds andApplications, Kluwer Academic Publishers, Dordrecht, (1996).
  • [2] Duggal, K., L., Sahin, B., Differential Geometry of Lightlike Submanifolds, Birkhauser Verlag AG, Germany, (2010).
  • [3] Liu, H., Curves in the lightlike cone, Contributions to Algebra and Geometry, 45 (2004), No. 1, pp. 291-303.
  • [4] Liu, H., and Meng, Q., Representation Formulas of Curves in a Two- and Three-Dimensional Lightlike Cone, 59 (2011), pp. 437-451.
  • [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] O’Neill, B., Semi-Riemannian Geometry, Academic Press, NewYork 1983. .Zbl 0531.53051 (1983).
  • [7] Sabuncuo ˘glu, A., Diferensiyel Geometri, Nobel Yayıncılık, Ankara. (2011).

Darboux Frame of a Curve Lying on a Lightlike Surface

Year 2016, , 121 - 130, 30.10.2016
https://doi.org/10.36753/mathenot.421465

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.

References

  • [1] Duggal, K., L., Bejancu, A., Lightlikesubmanifolds of Semi-Riemannian Manifolds andApplications, Kluwer Academic Publishers, Dordrecht, (1996).
  • [2] Duggal, K., L., Sahin, B., Differential Geometry of Lightlike Submanifolds, Birkhauser Verlag AG, Germany, (2010).
  • [3] Liu, H., Curves in the lightlike cone, Contributions to Algebra and Geometry, 45 (2004), No. 1, pp. 291-303.
  • [4] Liu, H., and Meng, Q., Representation Formulas of Curves in a Two- and Three-Dimensional Lightlike Cone, 59 (2011), pp. 437-451.
  • [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] O’Neill, B., Semi-Riemannian Geometry, Academic Press, NewYork 1983. .Zbl 0531.53051 (1983).
  • [7] Sabuncuo ˘glu, A., Diferensiyel Geometri, Nobel Yayıncılık, Ankara. (2011).
There are 7 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

E. Selcen Yakıcı Topbaş This is me

İsmail Gök

Nejat Ekmekci

Yusuf Yaylı

Publication Date October 30, 2016
Submission Date June 2, 2012
Published in Issue Year 2016

Cite

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 Topbaş ESY, Gök İ, Ekmekci N, Yaylı Y. Darboux Frame of a Curve Lying on a Lightlike Surface. Math. Sci. Appl. E-Notes. October 2016;4(2):121-130. doi:10.36753/mathenot.421465
Chicago Topbaş, E. Selcen Yakıcı, İsmail Gök, Nejat Ekmekci, and Yusuf Yaylı. “Darboux Frame of a Curve Lying on a Lightlike Surface”. Mathematical Sciences and Applications E-Notes 4, no. 2 (October 2016): 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 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, 2016, doi: 10.36753/mathenot.421465.
ISNAD Topbaş, E. Selcen Yakıcı et al. “Darboux Frame of a Curve Lying on a Lightlike Surface”. Mathematical Sciences and Applications E-Notes 4/2 (October 2016), 121-130. https://doi.org/10.36753/mathenot.421465.
JAMA 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, 2016, pp. 121-30, doi:10.36753/mathenot.421465.
Vancouver 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):121-30.

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