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

摘要

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