Chern number identities on compact complex surfaces and applications
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915447442505728 |
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| author | Yang, Xiaokui |
| author_facet | Yang, Xiaokui |
| contents | In this paper, we establish Chern number identities on compact complex surfaces. As an application, we prove that if $(M,g)$ is a compact Riemannian four-manifold with constant scalar curvature and admits a compatible complex structure $J$ such that the complexified Ricci curvature is a non-positive $(1,1)$ form, then $M$ is a Kähler surface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11171 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chern number identities on compact complex surfaces and applications Yang, Xiaokui Differential Geometry 53C55 In this paper, we establish Chern number identities on compact complex surfaces. As an application, we prove that if $(M,g)$ is a compact Riemannian four-manifold with constant scalar curvature and admits a compatible complex structure $J$ such that the complexified Ricci curvature is a non-positive $(1,1)$ form, then $M$ is a Kähler surface. |
| title | Chern number identities on compact complex surfaces and applications |
| topic | Differential Geometry 53C55 |
| url | https://arxiv.org/abs/2508.11171 |