On Ruled Surfaces Constructed by the Evolution of a Polynomial Space Curve

Abstract

In this paper, we present the evolutions of the ruled surfaces constructed by the tangent, normal-like, and binormal-like vector fields of a polynomial space curve. These evolutions of the ruled surfaces depend on the evolutions of their directrices using the Flc (Frenet like curve) frame along a polynomial space curve. Therefore, the evolutions of a polynomial curve are expressed in the first step of this study. Then, some geometric properties of the special ruled surfaces are investigated and examples of these surfaces are given and their graphics are drawn using the Mathematica 9 program.

Translation surfaces generating with some partner curve

“…The study of surfaces is one of the most captivating subjects in the field of differential geometry. Consequently, researchers have extensively investigated various types of surfaces [4][5][6]. Much like curves, researchers endeavor to characterize 166 A.…”