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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.16759 |
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| _version_ | 1866909590188195840 |
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| author | Abid, Fatima-Ezzahrae Benayadi, Said Boucetta, Mohamed Ouali, Hamza El Lebzioui, Hicham |
| author_facet | Abid, Fatima-Ezzahrae Benayadi, Said Boucetta, Mohamed Ouali, Hamza El Lebzioui, Hicham |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cyclic Riemannian Lie groups: description and curvatures Abid, Fatima-Ezzahrae Benayadi, Said Boucetta, Mohamed Ouali, Hamza El Lebzioui, Hicham Differential Geometry 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. |
| title | Cyclic Riemannian Lie groups: description and curvatures |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2504.16759 |