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arXiv · 1607.01950

On Locally Symmetric $3$-Dimensional Riemannian Lie Groups

Nimpa Pefoukeu Romain·Wouafo Kamga Jean·Djiadeu Ngaha Michel Bertrand
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Abstract

In this paper, we use the powerful tool Milnor bases to classify all the $3-$dimensional connected and locally symmetric Riemannian Lie Groups by solving system of polynomial equations of structure constants of each Lie algebra . Moreover, we showed that $E_0(2)$, is the only Lie group with locally symmetric left invariant Riemannian metrics which are not symmetric.

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Nimpa Pefoukeu Romain, Wouafo Kamga Jean, Djiadeu Ngaha Michel Bertrand. 2016-07-07. On Locally Symmetric $3$-Dimensional Riemannian Lie Groups. https://arxiv.org/abs/1607.01950

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