Cyclic Riemannian Lie groups: description and curvatures
Authors:
- Hicham LebziouiHLHicham Lebzioui
- Fatima-Ezzahrae AbidFAFatima-Ezzahrae Abid
- Saïd BenayadiSBSaïd Benayadi
- Hamza El OualiHOHamza El Ouali
Preprint
- 4 March 2026
- preprint
- Published by Elsevier in SSRN Electronic Journal
Abstract
A cyclic Riemannian Lie group is a Lie group G equipped with a left-invariant Riemannian metric h that satisfies HX,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. 176 (2015), 219239. 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.Keywords
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- On homogeneous manifolds of negative curvatureMathematische Annalen, 1974