Similar ruled surfaces with variable transformations in minkowski 3-space E3 1

Abstract

In this study, we consider the notion of similar ruled surface for timelike and spacelike ruled surfaces in Minkowski 3-space E31. We obtain some properties of these special surfaces in E31 and show that developable ruled surfaces in E31 form a family of similar ruled surfaces if and only if the striction curves of the surfaces are similar curves with variable transformation. Moreover, we obtain that cylindrical surfaces and conoids form two families of similar ruled surfaces in E31.