English

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 gg on the Lie group F4F^4. We classify Ricci solitons on (F4,g)(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 (F4,g)(F^4,g). Finally, we characterize a class of harmonic vector fields on (F4,g)(F^4,g).

Keywords

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}
}