The curvature and torsion: how to distinguish the shape of a curve 
Still curvature and torsion
When the curvature function has only isolated zeroes it is necessary to set the Frenet-Serret frame of the curve at all points with curvature 0, except for the end point. Note that the Frenet-Serret frame at a given instant is extremely useful because it provides information about the behaviour of the curve just after that instant. Therefore, the fact that the Frenet-Serret frame is set or not at the endpoint of the curve is not relevant.
