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arXiv · 2504.16759

Cyclic Riemannian Lie groups: description and curvatures

Fatima-Ezzahrae Abid·Said Benayadi·Mohamed Boucetta·Hamza El Ouali·Hicham Lebzioui
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Abstract

A cyclic Riemannian Lie group is a Lie group $G$ equipped with a left-invariant Riemannian metric $h$ that satisfies $\oint_{X,Y,Z}h([X,Y],Z)=0$ for any left-invariant vector fields $X,Y,Z$. The initial concept and exploration of these Lie groups were presented in Monatsh. Math. \textbf{176} (2015), 219-239. This paper builds upon the results from the aforementioned study by providing a complete description of cyclic Riemannian Lie groups and an in-depth analysis of their various curvatures.

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Fatima-Ezzahrae Abid, Said Benayadi, Mohamed Boucetta, Hamza El Ouali, Hicham Lebzioui. 2025-04-23. Cyclic Riemannian Lie groups: description and curvatures. https://arxiv.org/abs/2504.16759

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