On Ricci Solitons and Harmonic Vector Fields in the Thurston Geometry $F^4$
Differential Geometry
2026-03-11 v1
Abstract
In this paper, we consider a left-invariant Riemannian metric on the Lie group . We classify Ricci solitons on and show that all such solitons are expanding and non-gradient. Moreover, we study the existence of harmonic maps from compact Riemannian manifolds into . Finally, we characterize a class of harmonic vector fields on .
Cite
@article{arxiv.2603.08969,
title = {On Ricci Solitons and Harmonic Vector Fields in the Thurston Geometry $F^4$},
author = {Halima Boukhari and Hadjer Okbani and Ahmed Mohammed Cherif},
journal= {arXiv preprint arXiv:2603.08969},
year = {2026}
}