Open Access

ARTICLE

On Special Curves According to Darboux Frame in the Three Dimensional Lorentz Space

H. S. Abdel-Aziz¹, M. Khalifa Saad^1,2,*
1 Math. Dept., Faculty of Science, Sohag University, 82524 Sohag, Egypt .
2 Math. Dept., Faculty of Science, Islamic University of Madinah, 170 El -Madinah, KSA.
* Corresponding author: M. Khalifa Saad. Email: .

Computers, Materials & Continua 2018, 54(3), 229-249. https://doi.org/10.3970/cmc.2018.054.229

Abstract

In the light of great importance of curves and their frames in many different branches of science, especially differential geometry as well as geometric properties and the uses in various fields, we are interested here to study a special kind of curves called Smarandache curves in Lorentz 3-space. Then, we present some characterizations for these curves and calculate their Darboux invariants. Moreover, we classify TP, TU, PU and TPU-Smarandache curves of a spacelike curve according to the causal character of the vector, curve and surface used in the study. Besides, we give some of differential geometric properties and important relations between that curves. Finally, to demonstrate our theoretical results a computational example is given with graph.

---

Keywords

Smarandache curves, spacelike curve, timelike surface, Darboux frame.

---