On Kähler manifolds with non-negative mixed curvature
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916369651466240 |
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| author | Chu, Jianchun Lee, Man-Chun Zhu, Jintian |
| author_facet | Chu, Jianchun Lee, Man-Chun Zhu, Jintian |
| contents | In this work, we investigate compact Kähler manifolds with non-negative or quasi-positive mixed curvature coming from a linear combination of the Ricci and holomorphic sectional curvature, which covers various notions of curvature considered in the literature. Specifically, we prove a splitting theorem, analogous to the Cheeger-Gromoll splitting theorem, for complete Kähler manifolds with non-negative mixed curvature containing a line, and then establish a structure theorem for compact Kähler manifolds with non-negative mixed curvature. We also show that the Hodge numbers of compact Kähler manifolds with quasi-positive mixed curvature must vanish. Both results are based on the conformal perturbation method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14043 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Kähler manifolds with non-negative mixed curvature Chu, Jianchun Lee, Man-Chun Zhu, Jintian Differential Geometry Complex Variables In this work, we investigate compact Kähler manifolds with non-negative or quasi-positive mixed curvature coming from a linear combination of the Ricci and holomorphic sectional curvature, which covers various notions of curvature considered in the literature. Specifically, we prove a splitting theorem, analogous to the Cheeger-Gromoll splitting theorem, for complete Kähler manifolds with non-negative mixed curvature containing a line, and then establish a structure theorem for compact Kähler manifolds with non-negative mixed curvature. We also show that the Hodge numbers of compact Kähler manifolds with quasi-positive mixed curvature must vanish. Both results are based on the conformal perturbation method. |
| title | On Kähler manifolds with non-negative mixed curvature |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2408.14043 |