English

Cyclic Riemannian Lie groups: description and curvatures

Differential Geometry 2025-04-24 v1

Abstract

A cyclic Riemannian Lie group is a Lie group GG equipped with a left-invariant Riemannian metric hh that satisfies X,Y,Zh([X,Y],Z)=0\oint_{X,Y,Z}h([X,Y],Z)=0 for any left-invariant vector fields X,Y,ZX,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.

Keywords

Cite

@article{arxiv.2504.16759,
  title  = {Cyclic Riemannian Lie groups: description and curvatures},
  author = {Fatima-Ezzahrae Abid and Said Benayadi and Mohamed Boucetta and Hamza El Ouali and Hicham Lebzioui},
  journal= {arXiv preprint arXiv:2504.16759},
  year   = {2025}
}
R2 v1 2026-06-28T23:08:38.028Z