On rectifying curves in Euclidean 3-space

Authors : Sharief Deshmukh, Bang-yen Chen, Sana Hamoud Alshammari

Pages : 609-620

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Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :First, we study rectifying curves via the dilation of unit speed curves on the unit sphere $S^{2}$ in the Euclidean space $\mathbb E^3$. Then we obtain a necessary and sufficient condition for which the centrode $d(s)$ of a unit speed curve $\alpha(s)$ in $\mathbb E^3$ is a rectifying curve to improve a main result of \cite{cd05}. Finally, we prove that if a unit speed curve $\alpha(s)$ in $\mathbb E^3$ is neither a planar curve nor a helix, then its dilated centrode $\beta(s)=\rho(s) d(s)$, with dilation factor ${\rho}$, is always a rectifying curve, where $\rho$ is the radius of curvature of $\alpha$.
Keywords : Rectifying curve, centrode, spherical curve, dilated centrode