On rectifying curves in Euclidean 3-space

By Sharief Deshmukh, Bang‐Yen Chen, S. Alshammari. 2018

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First, we study rectifying curves via the dilation of unit speed curves on the unit sphere S in the Euclidean space E . Then we obtain a necessary and sufficient condition for which the centrode d(s) of a unit speed curve α(s) in E is a rectifying curve to improve a main result of [4]. Finally, we prove that if a unit speed curve α(s) in E is neither a planar curve nor a helix, then its dilated centrode β(s) = ρ(s)d(s) , with dilation factor ρ , is always a rectifying curve, where ρ is the radius of curvature of α .

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e1646757b242e611ad649b7aeda4f8e451d1254f