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In the present paper, we investigate special Smarandache curves with Darbouxapparatus with respect to Frenet and Darboux frame of an arbitrary curve on asurface in the three-dimensional Galilean space G3. Furthermore, we givegeneral position vectors of special Smarandache curves of geodesic, asymptoticand curvature line on the surface in G3. As a result of this, we provide somerelated examples of these curves.

Special Smarandache Curves with Respect to Darboux Frame in the Galilean 3-Space