November 9, 2025Open Access

Harmonic unit vector fields on 3-manifolds

Key Points

Harmonic unit vector fields exhibit totally geodesic integral curves on 3-manifolds, highlighting geometric roles.
Under specific curvature conditions, the study classifies these vector fields effectively.
Theoretical analysis references prior work on Riemannian flows and Killing vector fields within the framework of 3-manifolds.
Findings may illuminate geometric structures in manifold theory and inspire further research in this area.

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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