Harmonic unit vector fields on 3-manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917065362767872 |
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| author | Habib, Georges Savas-Halilaj, Andreas |
| author_facet | Habib, Georges Savas-Halilaj, Andreas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19756 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Harmonic unit vector fields on 3-manifolds Habib, Georges Savas-Halilaj, Andreas Differential Geometry 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. |
| title | Harmonic unit vector fields on 3-manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.19756 |