On Hermitian manifolds with vanishing curvature
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929447229194240 |
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| author | Broder, Kyle Tang, Kai |
| author_facet | Broder, Kyle Tang, Kai |
| contents | We show that Hermitian metrics with vanishing holomorphic curvature on compact complex manifolds with pseudoeffective canonical bundle are conformally balanced. Pluriclosed metrics with vanishing holomorphic curvature on compact Kähler manifolds are shown to be Kähler and hence, are completely classified. We prove that Hermitian metrics with vanishing real bisectional curvature on complex manifolds in the Fujiki class C are Kähler and thus fall under the same classification. Finally, we formalize the notion of `altered' curvatures, which force distinguished metric structures when mandated to coincide with their `standard' counterparts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_03666 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Hermitian manifolds with vanishing curvature Broder, Kyle Tang, Kai Differential Geometry Algebraic Geometry Complex Variables We show that Hermitian metrics with vanishing holomorphic curvature on compact complex manifolds with pseudoeffective canonical bundle are conformally balanced. Pluriclosed metrics with vanishing holomorphic curvature on compact Kähler manifolds are shown to be Kähler and hence, are completely classified. We prove that Hermitian metrics with vanishing real bisectional curvature on complex manifolds in the Fujiki class C are Kähler and thus fall under the same classification. Finally, we formalize the notion of `altered' curvatures, which force distinguished metric structures when mandated to coincide with their `standard' counterparts. |
| title | On Hermitian manifolds with vanishing curvature |
| topic | Differential Geometry Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2201.03666 |