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First, we study rectifying curves via the dilation of unit speed curves on the unit sphere S^2 in the Euclidean space E³. Then we obtain a necessary and sufficient condition for which the centrode d (s) of a unit speed curve (s) in E³ is a rectifying curve to improve a main result of cd05. Finally, we prove that if a unit speed curve (s) in E³ is neither a planar curve nor a helix, then its dilated centrode (s) = (s) d (s), with dilation factor, is always a rectifying curve, where is the radius of curvature of.
Deshmukh et al. (Sat,) studied this question.