Pseudo-Riemannian weakly symmetric manifolds of low dimension
We give a classification of pseudo-Riemannian weakly symmetric manifolds in dimensions and , based on the algebraic approach of such spaces through the notion of a pseudo-Riemannian weakly symmetric Lie algebra. We also study the general symmetry of reductive -dimensional pseudo-Riemannian weakly symmetric spaces and particularly prove that a -dimensional reductive -fold symmetric pseudo-Riemannian manifold must be globally symmetric.