Evolution of space-like curves and special time-like ruled surfaces in the Minkowski space

In this paper, we get the time evolution equations of curvature and torsion evolving spacelike curves in Minkowski space. Also, give inextensible evolutions timelike ruled surfaces that are produced by normal binormal vector fields curve derive necessary conditions for an inelastic surface evolution. Then, compute coefficients first second fundamental forms, Gauss mean curvatures special surfaces. As a result, applications terms velocities exact solutions these new equations.