Some special Smarandache ruled surfaces according to alternative frame in E3

Abstract

In this study ruled surfaces formed by alternative unit vectors that draw these curves along Smarandache curves obtained from alternative vectors and alternative unit Darboux vectors of a differentiable curve are defined. Then the Gaussian and mean curvatures of each ruled surface are computed. It is also examined whether the surfaces are developable or minimal. Finally, examples of these surfaces are given and their graphics are drawn.