On the Sabban frame belonging to involute-evolute curves

Abstract

In this paper, we investigate special Smarandache curves with regard to Sabban frame of involute curve. We create Sabban frame belonging to spherical indicatrix of involute curve. Smarandache curves are explained by Sabban vectors belonging to spherical indicatrix. Then, we calculate geodesic curvatures of this Smarandache curves. The results found for each curve is given depending on evolute curve. The example related to the subject is given and their figures are drawn with MAPPLE program.

Smarandache Curves of the Evolute Curve According to Sabban Frame

“…By definition, if the position vector of a curve is composed by the Frenet frame's vectors of another curve, then the curve is called a Smarandache curve [6]. Special Smarandache curves studied by some authors [1,2,5,6,7,8], and related reference therein [9,10,11]. Let α : I → E 3 be a unit speed curve denoted by the moving Frenet apparatus of {T, N, B, κ, τ}.…”

Harmonicity and differential equation of involute of a curve in E3

“…Therefore, many studies have been conducted in Euclidean and non-Euclidean spaces related to involute curves. To cite some examples Senyurt et al [3], Bulca et al [4], and Senyurt et al [5] are the works that have received considerable attention. Thanks to meticulous studies, it has been revealed that curves can be classified [6].…”