Cyclic Riemannian Lie groups: description and curvatures

2025/04/23 by Abid, Fatima-Ezzahrae, Benayadi, Said, Boucetta, Mohamed +2 · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.16759

Abstract

A cyclic Riemannian Lie group is a Lie group G equipped with a left-invariant Riemannian metric h that satisfies \oint_X,Y,Zh([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. 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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• Structure of non-solvable cyclic metric Lie algebras

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