A regular curve lies on a circular cylinder only if its curvature κ and torsion τ satisfy a specific compatibility ODE obtained from an eighth-degree polynomial condition on the angle function ψ.
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A necessary condition for cylindrical curves in terms of curvature and torsion
A regular curve lies on a circular cylinder only if its curvature κ and torsion τ satisfy a specific compatibility ODE obtained from an eighth-degree polynomial condition on the angle function ψ.