Beltrami theorem in Minkowski space

E. Beltrami proved a theorem on the relationship of curvatures for families of surfaces of revolution in the three-dimensional Euclidean space, which implies that if some surface of revolution $M'$ orthogonally intersects all surfaces obtained from a surface of constant curvature $M$ by translations along the rotation axis, then the curvature of the surface $M'$ is also constant and differs from the curvature of the surface $M$ only in sign. In this paper, we obtain analogs of this theorem for surfaces of revolution in the three-dimensional Minkowski space.