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.
Keywords:  pseudo-Riemannian manifold; pseudo-Riemannian weakly symmetric manifold; pseudo-Riemannian weakly symmetric Lie algebra; Lorentzian weakly symmetric manifold
Classification MSC:  53C30, 22E46


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Affiliations:   Bo Zhang, Zhiqi Chen, Shaoqiang Deng (correspodning author), School of Mathematical Sciences and LPMC, Nankai University, No. 94 Weijin Road, Nankai District, Tianjin 300071, P. R. China, e-mail: zhangbo@mail.nankai.edu.cn, chenzhiqi@nankai.edu.cn, dengsq@nankai.edu.cn


 
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