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| Main Author: | |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2012.04496 |
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| _version_ | 1866909753042534400 |
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| author | Yao, Qi |
| author_facet | Yao, Qi |
| contents | Let $G$ be a simply-connected semisimple compact Lie group, $X$ a compact Kähler manifold homogeneous under $G$, and $L$ a negative $G$-equivariant holomorphic line bundle over $X$. We prove that all $G$-invariant Kähler metrics on the total space of $L$ arise from the Calabi ansatz. Using this, we then show that there exists a unique $G$-invariant scalar-flat Kähler metric in each Kähler class of $L$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_04496 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Invariant scalar-flat Kähler metrics on line bundles over generalized flag varieties Yao, Qi Differential Geometry Let $G$ be a simply-connected semisimple compact Lie group, $X$ a compact Kähler manifold homogeneous under $G$, and $L$ a negative $G$-equivariant holomorphic line bundle over $X$. We prove that all $G$-invariant Kähler metrics on the total space of $L$ arise from the Calabi ansatz. Using this, we then show that there exists a unique $G$-invariant scalar-flat Kähler metric in each Kähler class of $L$. |
| title | Invariant scalar-flat Kähler metrics on line bundles over generalized flag varieties |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2012.04496 |