Harmonic maps from $S^3$ to $S^2$ and the rigidity of the Hopf fibration
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912851153649664 |
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| author | Georgakopoulos, Athanasios Magliaro, Marco Mari, Luciano Savas-Halilaj, Andreas |
| author_facet | Georgakopoulos, Athanasios Magliaro, Marco Mari, Luciano Savas-Halilaj, Andreas |
| contents | It was conjectured by Eells that the only harmonic maps $f : S^3 \to S^2$ are Hopf fibrations composed with conformal maps of $S^2$. We support this conjecture by proving its validity under suitable conditions on the Hessian and the singular values of $f$. Among the results, we obtain a pinching theorem in the spirit of that of Simons, Lawson and Chern, do Carmo and Kobayashi for minimal hypersurfaces in the sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16522 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Harmonic maps from $S^3$ to $S^2$ and the rigidity of the Hopf fibration Georgakopoulos, Athanasios Magliaro, Marco Mari, Luciano Savas-Halilaj, Andreas Differential Geometry It was conjectured by Eells that the only harmonic maps $f : S^3 \to S^2$ are Hopf fibrations composed with conformal maps of $S^2$. We support this conjecture by proving its validity under suitable conditions on the Hessian and the singular values of $f$. Among the results, we obtain a pinching theorem in the spirit of that of Simons, Lawson and Chern, do Carmo and Kobayashi for minimal hypersurfaces in the sphere. |
| title | Harmonic maps from $S^3$ to $S^2$ and the rigidity of the Hopf fibration |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2511.16522 |