# Pseudo-Riemannian weakly symmetric manifolds of low dimension

Bo Zhang; Zhiqi Chen; Shaoqiang Deng

Czechoslovak Mathematical Journal (2019)

- Volume: 69, Issue: 3, page 811-835
- ISSN: 0011-4642

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topZhang, Bo, Chen, Zhiqi, and Deng, Shaoqiang. "Pseudo-Riemannian weakly symmetric manifolds of low dimension." Czechoslovak Mathematical Journal 69.3 (2019): 811-835. <http://eudml.org/doc/294735>.

@article{Zhang2019,

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.},

author = {Zhang, Bo, Chen, Zhiqi, Deng, Shaoqiang},

journal = {Czechoslovak Mathematical Journal},

keywords = {pseudo-Riemannian manifold; pseudo-Riemannian weakly symmetric manifold; pseudo-Riemannian weakly symmetric Lie algebra; Lorentzian weakly symmetric manifold},

language = {eng},

number = {3},

pages = {811-835},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Pseudo-Riemannian weakly symmetric manifolds of low dimension},

url = {http://eudml.org/doc/294735},

volume = {69},

year = {2019},

}

TY - JOUR

AU - Zhang, Bo

AU - Chen, Zhiqi

AU - Deng, Shaoqiang

TI - Pseudo-Riemannian weakly symmetric manifolds of low dimension

JO - Czechoslovak Mathematical Journal

PY - 2019

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 69

IS - 3

SP - 811

EP - 835

AB - 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.

LA - eng

KW - pseudo-Riemannian manifold; pseudo-Riemannian weakly symmetric manifold; pseudo-Riemannian weakly symmetric Lie algebra; Lorentzian weakly symmetric manifold

UR - http://eudml.org/doc/294735

ER -

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