A note on Einstein metrics and Riemannian twistor spaces
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913952391233536 |
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| author | Dameno, Davide |
| author_facet | Dameno, Davide |
| contents | Inspired by the problem of classifying Einstein manifolds with positive scalar curvature, we prove that an Einstein four-manifold whose associated twistor space has scalar curvature constant on the fibers of the twistor bundle is half conformally flat: in particular, the only compact Einstein four-manifolds with positive scalar curvature satisfying this twistorial condition are $\mathbb{S}^4$ and $\mathbb{CP}^2$. We also generalize a well-known result due to Friedrich and Grunewald, providing a classification of complete four-manifolds whose twistor space is Ricci parallel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16113 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on Einstein metrics and Riemannian twistor spaces Dameno, Davide Differential Geometry Inspired by the problem of classifying Einstein manifolds with positive scalar curvature, we prove that an Einstein four-manifold whose associated twistor space has scalar curvature constant on the fibers of the twistor bundle is half conformally flat: in particular, the only compact Einstein four-manifolds with positive scalar curvature satisfying this twistorial condition are $\mathbb{S}^4$ and $\mathbb{CP}^2$. We also generalize a well-known result due to Friedrich and Grunewald, providing a classification of complete four-manifolds whose twistor space is Ricci parallel. |
| title | A note on Einstein metrics and Riemannian twistor spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2507.16113 |