Negatively curved Kähler metrics on total spaces of a class of vector bundles
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909905003216896 |
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| author | Wu, Hanyu Yang, Bo |
| author_facet | Wu, Hanyu Yang, Bo |
| contents | In this paper we show an abundance of complete Kähler metrics with negative holomorphic bisectional curvature on total spaces of certain vector bundles. Assume that such total spaces are endowed with a wider class of nonpositively curved Kähler metrics. We prove dimension estimates on holomorphic functions on these manifolds, as well as Liouville theorems for holomorphic mappings between them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_16354 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Negatively curved Kähler metrics on total spaces of a class of vector bundles Wu, Hanyu Yang, Bo Differential Geometry 32Q05, 32Q15, and 53C55 In this paper we show an abundance of complete Kähler metrics with negative holomorphic bisectional curvature on total spaces of certain vector bundles. Assume that such total spaces are endowed with a wider class of nonpositively curved Kähler metrics. We prove dimension estimates on holomorphic functions on these manifolds, as well as Liouville theorems for holomorphic mappings between them. |
| title | Negatively curved Kähler metrics on total spaces of a class of vector bundles |
| topic | Differential Geometry 32Q05, 32Q15, and 53C55 |
| url | https://arxiv.org/abs/2508.16354 |