On Ruled Surfaces with a Sannia Frame in Euclidean 3-space

Abstract

In this paper we define a new family of ruled surfaces using an othonormal Sannia frame defined on a base consisting of the striction curve of the tangent, the princi-pal normal, the binormal and the Darboux ruled surface. We examine characterizations of these surfaces by first and second fundamental forms, and mean and Gaussian curvatures. Based on these characterizations, we provide conditions under which these ruled surfaces are developable and minimal. Finally, we present some examples and pictures of each of the corresponding ruled surfaces.