On A Time-like Ruled Surface With Time-like Rulings In Minkowski3-space

Let M be a time-like ruled surface with space-like striction curve and time-like rulings in Minkowski3-space. When the distribution parameter on M is constant, we obtain an explicit representation of M in terms of a system of one order ordinary differential equations. And we compute the geodesic curvature of a curve on that surface and discuss the solvability of the geodesic equations. We also discuss the mean curvature of M with constant distribution parameter and prove that M has constant mean curvature if and only if it is maximal. Finally, we obtain a description of maximal surfaces in this class of surfaces.