Geodesic
Pseudo-Riemannian weakly symmetric manifolds of low dimension
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 811-835
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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.
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.
DOI : 10.21136/CMJ.2019.0515-17
Classification : 22E46, 53C30
Keywords: pseudo-Riemannian manifold; pseudo-Riemannian weakly symmetric manifold; pseudo-Riemannian weakly symmetric Lie algebra; Lorentzian weakly symmetric manifold 
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Zhang, Bo; Chen, Zhiqi; Deng, Shaoqiang. Pseudo-Riemannian weakly symmetric manifolds of low dimension. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 811-835. doi: 10.21136/CMJ.2019.0515-17

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