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arXiv · 2510.19756

Harmonic unit vector fields on 3-manifolds

Georges Habib·Andreas Savas-Halilaj
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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.

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Georges Habib, Andreas Savas-Halilaj. 2025-10-22. Harmonic unit vector fields on 3-manifolds. https://arxiv.org/abs/2510.19756

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