Holonomy and the Ricci curvature of complex Hermitian manifolds
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929533578379264 |
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| author | Ni, Lei |
| author_facet | Ni, Lei |
| contents | We prove two results on geometric consequences of the representation of restricted holonomy group of a Hermitian connection. The first result concerns when such a Hermitian manifold is Kähler in terms of the torsion and the irreducibility of the holonomy action. As a consequence we obtain a criterion of when a Hermitian manifold (and connection) is a generalized Calabi-Yau (in the sense that the Chern Ricci vanishes or equivalently that the restricted holonomy is inside $\mathsf{SU}(m)$). The second result concerns when a compact Kähler manifold with a generic restricted holonomy group is projective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06411 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holonomy and the Ricci curvature of complex Hermitian manifolds Ni, Lei Differential Geometry Mathematical Physics 53C23, 53C55 We prove two results on geometric consequences of the representation of restricted holonomy group of a Hermitian connection. The first result concerns when such a Hermitian manifold is Kähler in terms of the torsion and the irreducibility of the holonomy action. As a consequence we obtain a criterion of when a Hermitian manifold (and connection) is a generalized Calabi-Yau (in the sense that the Chern Ricci vanishes or equivalently that the restricted holonomy is inside $\mathsf{SU}(m)$). The second result concerns when a compact Kähler manifold with a generic restricted holonomy group is projective. |
| title | Holonomy and the Ricci curvature of complex Hermitian manifolds |
| topic | Differential Geometry Mathematical Physics 53C23, 53C55 |
| url | https://arxiv.org/abs/2410.06411 |