On Spatial Quaternionic Involute Curve A New View

Abstract

In this study, the normal vector and the unit Darboux vector of spatial involute curve of the spatial quaternionic curve are taken as the position vector, the curvature and torsion of obtained smarandahce curve were calculeted.Mathematics Subject Classification. 53A04, 53C26.

Generalized quaternionic involute‐evolute curves in the Euclidean four‐space E4

“…Taking the inner product on both sides of Equation (9) with N and B 2 , it follows ′ = 0 and ′ = 0, which means that and are constants. So Equation (9) takes the form…”

“…Keçilio lu and İlarslan studied the quaternionic Bertrand curves in Euclidean four‐space . By considering the Darboux vector, Şenyurt et al studied spatial quaternionic involute curves in the three‐dimensional space . Şahiner gave the definition and characterizations of quaternionic direction curves .…”

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}.…”

The dual spatial quaternionic expression of ruled surfaces

“…Shoemake's paper is that it took the concept of the orientation frame for moving 3-D objects and cameras, and the introduced quaternions to animators as a solution. Many studies have been made on quaternionic and dual quaternionic curves, such as [2][3][4][5][6].…”