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

Halima Boukhari, Hadjer Okbani, Ahmed Mohammed Cherif

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…