Darboux Frame of a Curve Lying on a Lightlike Surface

Yıl 2016, Cilt: 4 Sayı: 2, 121 - 130, 30.10.2016

E. Selcen Yakıcı Topbaş İsmail Gök Nejat Ekmekci Yusuf Yaylı

https://doi.org/10.36753/mathenot.421465

Cited By: 4

Öz

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.

Anahtar Kelimeler

Darboux frame, Lightlike surface, Lightlike cone, Helix

Kaynakça

• [1] Duggal, K., L., Bejancu, A., Lightlikesubmanifolds of Semi-Riemannian Manifolds andApplications, Kluwer Academic Publishers, Dordrecht, (1996).
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• [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).