Notes on the Curves in Lorentzian Plane L2

In this study, position vector of a Lorentzian plane curve (space-like or timelike, i.e.) is investigated. First, a system of differential equation whose solution gives the components of the position vector on the Frenet axis is constructed. By means of solution of mentioned system, position vector of all such curves according to Frenet frame is obtained. Thereafter, it is proven that, position vector and curvature of a Lorentzian plane curve satisfy a vector differential equation of third order. Moreover, using this result, position vector of such curves with respect to standard frame is presented. By this way, we present a short contribution to Smarandache geometries.