Non-degenerate surfaces of revolution in Minkowski space that satisfy the relation aH+bK=c

In this work, we study spacelike and timelike surfaces of revolution in Minkowski space $\e_{1}^{3}$ that satisfy $aH+bK=c$, where $H$ and $K$ denote the mean curvature and the Gauss curvature of the surface and $a$, $b$ and $c$ are constants. The classification depends on the causal character of the axis of revolution and in all the cases, we obtain a first integral of the equation of the generating curve of the surface.