Hermitian geometrically formal manifolds
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916842820337664 |
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| author | Sferruzza, Tommaso Tomassini, Adriano |
| author_facet | Sferruzza, Tommaso Tomassini, Adriano |
| contents | We study Hermitian geometrically formal metrics on compact complex manifolds, focusing on Dolbeault, Bott-Chern, and Aeppli cohomologies. We establish topological and cohomological obstructions to their existence and we provide a detailed analysis for compact complex surfaces, complex parallelisable solvmanifolds, and Calabi-Eckmann manifolds. We prove that the standard blow-up metric on any blow-up of a Kähler manifold is not geometrically formal, and that Kähler metrics with nonnegative curvature operator are necessarily geometrically formal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hermitian geometrically formal manifolds Sferruzza, Tommaso Tomassini, Adriano Differential Geometry 53C55, 32Q55, 55P99, 58A14 We study Hermitian geometrically formal metrics on compact complex manifolds, focusing on Dolbeault, Bott-Chern, and Aeppli cohomologies. We establish topological and cohomological obstructions to their existence and we provide a detailed analysis for compact complex surfaces, complex parallelisable solvmanifolds, and Calabi-Eckmann manifolds. We prove that the standard blow-up metric on any blow-up of a Kähler manifold is not geometrically formal, and that Kähler metrics with nonnegative curvature operator are necessarily geometrically formal. |
| title | Hermitian geometrically formal manifolds |
| topic | Differential Geometry 53C55, 32Q55, 55P99, 58A14 |
| url | https://arxiv.org/abs/2507.10263 |