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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2601.15008 |
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| _version_ | 1866918298839416832 |
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| author | Ayad, Youssef |
| author_facet | Ayad, Youssef |
| contents | We investigate the conditions under which pseudo-Riemannian inner products induce pseudo-Riemannian algebraic Ricci solitons on four-dimensional Lie algebras. By analyzing the algebraic Ricci soliton equation for each four-dimensional Lie algebra, we obtain a complete description of when such pseudo-Riemannian algebraic Ricci solitons arise in dimension four. We present two applications of our formalism on a chosen four-dimensional Lie algebra by exhibiting a pseudo-Riemannian algebraic Ricci soliton and a flat pseudo-Riemannian inner product, which is a trivial algebraic Ricci soliton. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15008 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pseudo-Riemannian Algebraic Ricci Solitons on Four-Dimensional Lie Groups Ayad, Youssef Differential Geometry 17B60, 17B40, 53C50 We investigate the conditions under which pseudo-Riemannian inner products induce pseudo-Riemannian algebraic Ricci solitons on four-dimensional Lie algebras. By analyzing the algebraic Ricci soliton equation for each four-dimensional Lie algebra, we obtain a complete description of when such pseudo-Riemannian algebraic Ricci solitons arise in dimension four. We present two applications of our formalism on a chosen four-dimensional Lie algebra by exhibiting a pseudo-Riemannian algebraic Ricci soliton and a flat pseudo-Riemannian inner product, which is a trivial algebraic Ricci soliton. |
| title | Pseudo-Riemannian Algebraic Ricci Solitons on Four-Dimensional Lie Groups |
| topic | Differential Geometry 17B60, 17B40, 53C50 |
| url | https://arxiv.org/abs/2601.15008 |