English

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!

R2 v1 2026-07-01T07:00:07.925Z