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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2510.05546 |
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| _version_ | 1866914085186043904 |
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| author | Chen, Weiguo Tang, Kai |
| author_facet | Chen, Weiguo Tang, Kai |
| contents | In this paper, we consider general $k$th-mixed curvature $\mathcal{C}^{(k)}_{α,β}$ ($β\neq0$) for Hermitian manifolds, which is a convex combination of the $k$th Chern Ricci curvature and holomorphic sectional curvature. We prove that any compact Hermitian surface with constant $k$th-mixed curvature is self-dual. Furthermore, we show that if a compact Hermitian surface has constant 2th-mixed curvature $c$, then the Hermitian metric must be Kähler. For the higher-dimensional case, when the parameters $α$ and $β$ satisfy certain conditions, we can also obtain partial results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05546 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constant $k$th-mixed curvature Chen, Weiguo Tang, Kai Differential Geometry 53C55 In this paper, we consider general $k$th-mixed curvature $\mathcal{C}^{(k)}_{α,β}$ ($β\neq0$) for Hermitian manifolds, which is a convex combination of the $k$th Chern Ricci curvature and holomorphic sectional curvature. We prove that any compact Hermitian surface with constant $k$th-mixed curvature is self-dual. Furthermore, we show that if a compact Hermitian surface has constant 2th-mixed curvature $c$, then the Hermitian metric must be Kähler. For the higher-dimensional case, when the parameters $α$ and $β$ satisfy certain conditions, we can also obtain partial results. |
| title | Constant $k$th-mixed curvature |
| topic | Differential Geometry 53C55 |
| url | https://arxiv.org/abs/2510.05546 |