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arXiv · 2603.08969

On Ricci Solitons and Harmonic Vector Fields in the Thurston Geometry $F^4$

Halima Boukhari·Hadjer Okbani·Ahmed Mohammed Cherif
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Abstract

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 $(F^4,g)$.

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Halima Boukhari, Hadjer Okbani, Ahmed Mohammed Cherif. 2026-03-09. On Ricci Solitons and Harmonic Vector Fields in the Thurston Geometry $F^4$. https://arxiv.org/abs/2603.08969

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