Abstract
The following result is proved: a 3-dimensional connected and simply connected Riemannian manifold admitting a reduced Σ-structure (in the sense of O. Loos) is either a Riemannian symmetric space or it is isometric to a unimodular Lie group with a left-invariant Riemannian metric. At the same time, we give first nontrivial examples of Riemannian Σ-spaces, which are not “symmetric of finite order”.
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Kowalski, O., Sekizawa, M. On 3-dimensional Riemannian Σ-spaces. Monatshefte für Mathematik 103, 303–320 (1987). https://doi.org/10.1007/BF01318071
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DOI: https://doi.org/10.1007/BF01318071