On Ricci Solitons and Harmonic Vector Fields in the Thurston Geometry $F^4$
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 $(F^4,g)$.
Fields of Study & Subjects
Advanced Differential Geometry Research
Geometric Analysis and Curvature Flows
Geometry and complex manifolds
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 9 March 2026
- Language
- EN
- Document type
- Preprint