Investigating the skills of junior high school students in posing problems in field of proportional reasoning

In this paper, we investigate the Einsteinian manifolds with parallel null distribution. For this purpose, we first obtain the equations, which are known as Einstein's equations, that lead to finding the mentioned manifolds and then, we reduce Einstein's equations by using Lie symmetry method. In this method, we first obtain the generators of the symmetry algebra and then calculate the differential Invariants for each of the generators and calculate the group invariant solutions of this equation. We also obtain the optimal system of the one-dimensional sub-algebras of these equations which helps us to have a classification on group invariant solutions by using conjugate mapping.