Four-dimensional pseudo-Riemannian g.o. spaces and manifolds

We prove that apart from the already classified non-reductive examples (Calvaruso et al., 2015), any four-dimensional pseudo-Riemannian g.o. manifold is naturally reductive. To obtain this result, we shall also provide a complete description up to isometries of four-dimensional pseudo-Riemannian g.o. spaces, and show explicit realizations of the four-dimensional pseudo-Riemannian naturally reductive spaces classified in Batat et al. (2015).