Czechoslovak Mathematical Journal, Vol. 69, No. 3, pp. 811-835, 2019
Pseudo-Riemannian weakly symmetric manifolds of low dimension
Bo Zhang, Zhiqi Chen, Shaoqiang Deng
Received November 10, 2017. Published online March 26, 2019.
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.