Image Curves on the Parallel-Like Surfaces in E3

In this paper, it's introduced the curves lying on parallel-like surface Mf of a surface M in Euclidean space. Taking into account the definition of the parallel-like surface it's obtained parametric expression of these curves and examinated Darboux frame for these curves which we call image curves. And finally the curves lying on the surfaces M and Mf are compared by considering their geodesic and normal curvatures, the geodesic torsion.