Before revision:  Finally, we also address in this work the problem of characterizing those curves whose position vector  , up to a translation, lies on a (moving ) plane spanned by the unit tangent and a rotation minimizing vector fieldand prove that they are precisely the plane curves .
After revision:  Finally, we also address in this work the problem of characterizing those curves whose position vector , up to a translation, lies on a (moving ) plane spanned by the unit tangent and an RM vector field. Finally, as an application, we characterize Bertrand curves as curves whose so-called natural mates are spherical .