Before revision:  Finally, since Frenet frames and osculating spheres are not well defined at the zeros of the curvature and torsion , respectively, we discuss the behavior of the angle between the principal normal and a rotation minimizing vectornear these zeros. For a curve whose torsion vanishes on intervals or isolated points only, we show that a rotation minimizing frame can be globally defined using our procedure by conveniently choosing some arbitrary constants. On the other hand, we mention that rotation minimizing frames can be well defined via their Frenet frames for analytic curves. Certainly, our approach will be of great importance in those contexts where rotation minimizing frames play a role .
After revision:  Finally, since Frenet frames and osculating spheres are not well defined at the zeros of the curvature and torsion , respectively, we discuss the behavior of the unit tangent and a rotation minimizing vector field and prove that they are precisely the plane curves .