Generalized Ruled Surfaces in Myller Configuration

Abstract

In this paper, we introduce a quite big ruled surface family, which is called generalized ruled surfaces with Frenet frame in Myller configuration for Euclidean 3-space. This paper especially improves the theory of surfaces with respect to ruled surfaces and presents the relationships between the usual theory of curves and the theory of surfaces with Myller configuration. We investigate some special type ruled surfaces, such as rectifying-type ruled surfaces, osculating-type ruled surfaces, tangent-type ruled surfaces and trajectory ruled surfaces with Frenet frame in Myller configuration for $E_3$. We also give some particular cases of these ruled surfaces, as well. Since the geometry of versor fields along a curve with Frenet-type frame in Myller configuration for $E_3$ is a generalization of the usual theory of curves in classical Euclidean space, the surface theory of versor fields along a curve with Frenet-type frame in Myller configuration for $E_3$ is a generalization of the usual theory of surfaces in classical Euclidean space, as well. Then, we establish some numerical examples with some illustrative figures with respect to the ruled surfaces in Myller configuration in order to solidify and concretize the given results.