Czechoslovak Mathematical Journal | 2019
Pseudo-Riemannian weakly symmetric manifolds of low dimension
Abstract
We give a classification of pseudo-Riemannian weakly symmetric manifolds in dimensions 2 and 3, 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 3-dimensional pseudo-Riemannian weakly symmetric spaces and particularly prove that a 3-dimensional reductive 2-fold symmetric pseudo-Riemannian manifold must be globally symmetric.