Harmonic unit vector fields on 3-manifolds

2025/10/22 by Georges Habib, Habib, Georges, Andreas Savas-Halilaj +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2510.19756

openalex publication_date 2025/10/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

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.

Citations

• Gauss maps of harmonic and minimal great circle fibrations
• Harmonic Vector Fields on Space Forms
• Energy and volume of vector fields on spherical domains
• Curvatures of left invariant metrics on lie groups

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