On Ricci Solitons and Harmonic Vector Fields in the Thurston Geometry $F^4$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917327859089408 |
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| author | Boukhari, Halima Okbani, Hadjer Cherif, Ahmed Mohammed |
| author_facet | Boukhari, Halima Okbani, Hadjer Cherif, Ahmed Mohammed |
| contents | In this paper, we consider a left-invariant Riemannian metric $g$ on the Lie group $F^4$. We classify Ricci solitons on $(F^4,g)$ and show that all such solitons are expanding and non-gradient. Moreover, we study the existence of harmonic maps from compact Riemannian manifolds into $(F^4,g)$. Finally, we characterize a class of harmonic vector fields on $(F^4,g)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08969 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Ricci Solitons and Harmonic Vector Fields in the Thurston Geometry $F^4$ Boukhari, Halima Okbani, Hadjer Cherif, Ahmed Mohammed Differential Geometry In this paper, we consider a left-invariant Riemannian metric $g$ on the Lie group $F^4$. We classify Ricci solitons on $(F^4,g)$ and show that all such solitons are expanding and non-gradient. Moreover, we study the existence of harmonic maps from compact Riemannian manifolds into $(F^4,g)$. Finally, we characterize a class of harmonic vector fields on $(F^4,g)$. |
| title | On Ricci Solitons and Harmonic Vector Fields in the Thurston Geometry $F^4$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2603.08969 |