2016 # 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.

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“…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…”

confidence: 99%

“…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…”

confidence: 99%

“…Keçilio $\stackrel{\u02c7}{\mathrm{normalg}}$ 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 .…”

confidence: 99%

“…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}.…”

confidence: 99%

“…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].…”

confidence: 99%