Curves as a subject of differential geometry have been intriguing for researchers throughout mathematical history and so they have been one of the interesting research fields. Regular curves play a central role in the theory of curves in differential geometry. In the theory of curves, there are some special curves such as Bertrand curves, Mannheim curves, involute and evolute curves, and pedal ...

In this paper, we introduce special Smarandache curves according to Sabban frame on S and we give some characterization of Smarandache curves. Besides, we illustrate examples of our results. Mathematics Subject Classification (2010): 53A04, 53C40.

‎in this work‎, ‎first the differential equation characterizing position vector‎ ‎of spacelike curve is obtained in lorentzian plane $mathbb{l}^{2}.$ then the‎ ‎special curves mentioned above are studied in lorentzian plane $mathbb{l}%‎‎^{2}.$ finally some characterizations of these special curves are given in‎ ‎$mathbb{l}^{2}.$‎

In this paper, we introduce new adjoint curves which are associated in Euclidean space of three dimension. They generated with the help integral special Smarandache curves. We attain some connections between Frenet apparatus these and main curve. characterize conditions they general helix slant helix. Finally, exemplify them figures.

In this paper, the invariants of Smarandache curves, which consist Frenet vectors involute curve, are calculated in terms evolute curve.