Lorentzian Darboux images of curves on spacelike surfaces in   Lorentz-Minkowski 3-space
  For a regular curve on a spacelike surface in Lorentz-Minkowski $3$-space, we have a moving frame along the curve which is called a Lorentzian Darboux frame. We introduce five special vector fields along the curve associated to the Lorentzian Darboux frame and investigate their singularities. 
Noriaki Ito and Shyuichi Izumiya
math.DG