Rectifying curves in Euclidean spaces are geodesics on higher-dimensional cones, and a formal map links them to spherical curves.
Rectifying curves in the n -dimensional Euclidean space, Turk
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Curves orthogonal to a vector field in Euclidean spaces
Rectifying curves in Euclidean spaces are geodesics on higher-dimensional cones, and a formal map links them to spherical curves.