Scalar Curvature in Dimension 4
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909963178213376 |
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| author | Deng, Jialong |
| author_facet | Deng, Jialong |
| contents | We prove that every locally conformally flat metric on a closed, oriented hyperbolic 4-manifold with scalar curvature bounded below by -12 satisfies Schoen's conjecture. We also classify all closed Riemannian 4-manifolds of positive scalar curvature that arise as total spaces of fibre bundles. For a closed locally conformally flat 4-manifold with scalar curvature zero and nontrivial second homotopy group, we show that its universal Riemannian cover is homothetic to the standard product of the hyperbolic plane and the round 2-sphere. This affirmatively answers a question of N. H. Noronha. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Scalar Curvature in Dimension 4 Deng, Jialong Differential Geometry We prove that every locally conformally flat metric on a closed, oriented hyperbolic 4-manifold with scalar curvature bounded below by -12 satisfies Schoen's conjecture. We also classify all closed Riemannian 4-manifolds of positive scalar curvature that arise as total spaces of fibre bundles. For a closed locally conformally flat 4-manifold with scalar curvature zero and nontrivial second homotopy group, we show that its universal Riemannian cover is homothetic to the standard product of the hyperbolic plane and the round 2-sphere. This affirmatively answers a question of N. H. Noronha. |
| title | Scalar Curvature in Dimension 4 |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.13528 |