Some special ruled surfaces and parallel surfaces of these surfaces

In this thesis, it is established the relations between the curvatures of the surfaces by obtaining parallel surfaces of the ruled surfaces in Euclidean 3-space. Specifically, the parallel surfaces of the non-developable ruled surfaces that the base curve is the striction line of the ruled surfaces are obtained. In this case, it is proved that to be ruled surface under which condition of the obtained parallel surfaces. Again, in this case it is shown that relations between the curvatures of the surfaces are more special. Besides, it is proved that striction line is helix, slant helix, Bertrand or Mannheim curve in some special cases. Finally, the ımage of the striction line on the parallel surfaces is obtained and these curves are examined in terms of the differential geometry.