Dual Smarandache Curves and Smarandache Ruled Surfaces
  In this paper, by considering dual geodesic trihedron (dual Darboux frame) we define dual Smarandache curves lying fully on dual unit sphere S^2 and corresponding to ruled surfaces. We obtain the relationships between the elements of curvature of dual spherical curve (ruled surface) x(s) and its dual Smarandache curve (Smarandache ruled surface) x1(s) and we give an example for dual Smarandache curves of a dual spherical curve. 
Tanju Kahraman, Mehmet \"Onder, H. H\"useyin U\u{g}urlu
math.GM