On Locally Symmetric $3$-Dimensional Riemannian Lie Groups

Nimpa Pefoukeu Romain; Wouafo Kamga Jean; Djiadeu Ngaha Michel Bertrand

On Locally Symmetric $3$-Dimensional Riemannian Lie Groups

Differential Geometry 2016-07-08 v1

Authors: Nimpa Pefoukeu Romain , Wouafo Kamga Jean , Djiadeu Ngaha Michel Bertrand

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.

Keywords

locally symmetric Riemannian Lie groups Milnor bases structure constants polynomial equations left invariant metrics 3-dimensional

Cite

@article{arxiv.1607.01950,
  title  = {On Locally Symmetric $3$-Dimensional Riemannian Lie Groups},
  author = {Nimpa Pefoukeu Romain and Wouafo Kamga Jean and Djiadeu Ngaha Michel Bertrand},
  journal= {arXiv preprint arXiv:1607.01950},
  year   = {2016}
}

Comments

$16$ pages, $3$ Tables

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