Abstract:In this paper, we study rectifying curves arising through the dilation of unit speed curves on the unit sphere S 3 and conclude that arcs of great circles on S 3 do not dilate to rectifying curves, which develope previously obtained results for rectifying curves in Eucidean spaces. This fact allows us to prove that there exists an associated rectifying curve for each Frenet curve in the Euclidean space E 4 and a result of the fact rectifying curves in the Euclidean space E 4 are ample , indeed as an appication… Show more
“…If a curve is a Frenet curve, then its curvature κ > 0 and torsion τ=0. These curves are studied in [3,4,5,6,7] by many geometers. Some important kinds of these curves are rectifying curves, slant helices characterized in [10,11].…”
For each non-null Frenet curve in Minkowski 3-space, there exists a unique unit speed non-null curve ̅ tangent to the principal binormal vector field of . We briefly call this curve ̅ the conjugate mate of . The aim of this paper is to prove some relationships between a non-null Frenet curve and its non-null conjugate mate.
“…If a curve is a Frenet curve, then its curvature κ > 0 and torsion τ=0. These curves are studied in [3,4,5,6,7] by many geometers. Some important kinds of these curves are rectifying curves, slant helices characterized in [10,11].…”
For each non-null Frenet curve in Minkowski 3-space, there exists a unique unit speed non-null curve ̅ tangent to the principal binormal vector field of . We briefly call this curve ̅ the conjugate mate of . The aim of this paper is to prove some relationships between a non-null Frenet curve and its non-null conjugate mate.
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