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Pseudo-Riemannian weakly symmetric manifolds of low dimension. (English) Zbl 07088818
Summary: 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.
MSC:
53C30 Differential geometry of homogeneous manifolds
22E46 Semisimple Lie groups and their representations
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