Constant Angle Ruled Surfaces with a Pointwise 1-Type Gauss Map

Abstract

In this study, constant angle ruled surfaces with a pointwise 1-type Gauss map, which is very useful in the classification of surfaces, are investigated in terms of the Frenet elements of the base curves of the ruled surfaces in Euclidean 3-space. In order to form a basis for our work, firstly, basic concepts related to the Gauss map of an oriented surface are given. Later, a classification is satisfied by determining the necessary conditions to be the first kind, the second kind, and the harmonic of the pointwise 1-type of the Gauss map for these surfaces. Finally, some examples of these surfaces are provided, and their graphical illustrations are displayed.