Abstract
In this paper we analyzed the problem of studying locally the scalar curvature S of the three dimensional kinematic surfaces obtained by the homothetic motion of a helix in Lorentz-Minkowski space ET. We express the scalar curvature S of the corresponding kinematic surfaces as the quotient of hyperbolic functions {cosh m phi, sinh m phi}, and we derive the necessary and sufficient conditions for the coefficients to vanishes identically. Finally, an example is given to show three dimensional kinematic surfaces with zero scalar curvature.