Harmonic unit vector fields on 3-manifolds
Differential Geometry
2025-11-07 v2
Abstract
We investigate harmonic unit vector fields with totally geodesic integral curves on 3-manifolds. Under mild curvature assumptions, we classify both the vector fields and the manifolds that support them. Our results are inspired by Carriere's classification of Riemannian flows on compact three-manifolds, as well as by the works of Geiges and Belgun on Killing vector fields on Sasakian manifolds.
Keywords
Cite
@article{arxiv.2510.19756,
title = {Harmonic unit vector fields on 3-manifolds},
author = {Georges Habib and Andreas Savas-Halilaj},
journal= {arXiv preprint arXiv:2510.19756},
year = {2025}
}
Comments
Typos fixed!