Riemannian Geometry of Lie Groups with One and Two-Dimensional Commutator Subgroups
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909991930167296 |
|---|---|
| author | Moghaddam, Hamid Reza Salimi |
| author_facet | Moghaddam, Hamid Reza Salimi |
| contents | In this paper, we investigate left invariant Riemannian metrics on Lie groups with one and two-dimensional commutator subgroups. We explicitly provide the Levi-Civita connection, sectional curvature, and Ricci curvature, and we give computable necessary and sufficient conditions for these Riemannian manifolds to be Ricci solitons. Furthermore, we characterize all Ricci solitons on Lie groups with one-dimensional commutator subgroups. In the final section, we examine the results concerning all indecomposable Lie groups with two-dimensional commutator subgroups of dimension greater than or equal to five. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10730 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Riemannian Geometry of Lie Groups with One and Two-Dimensional Commutator Subgroups Moghaddam, Hamid Reza Salimi Differential Geometry 53C30, 53C21, 22E60 In this paper, we investigate left invariant Riemannian metrics on Lie groups with one and two-dimensional commutator subgroups. We explicitly provide the Levi-Civita connection, sectional curvature, and Ricci curvature, and we give computable necessary and sufficient conditions for these Riemannian manifolds to be Ricci solitons. Furthermore, we characterize all Ricci solitons on Lie groups with one-dimensional commutator subgroups. In the final section, we examine the results concerning all indecomposable Lie groups with two-dimensional commutator subgroups of dimension greater than or equal to five. |
| title | Riemannian Geometry of Lie Groups with One and Two-Dimensional Commutator Subgroups |
| topic | Differential Geometry 53C30, 53C21, 22E60 |
| url | https://arxiv.org/abs/2601.10730 |