Bergman metrics as pull-backs of the Fubini-Study metric
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866914789578506240 |
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| author | Huang, Xiaojun Li, Song-Ying |
| author_facet | Huang, Xiaojun Li, Song-Ying |
| contents | Domains and more generally complex manifolds whose Bergman metrics have constant holomorphic sectional curvature are characterized. Our approach is to treat the Bergman metrics as the pull-back by the Bergman-Bochner maps of the Fubini-Study metric of the complex projective space of infinite dimension. Several new domains with surprising curvature properties for their Bergman metrics are constructed. A new conjecture is also formulated at the end of the paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_13456 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bergman metrics as pull-backs of the Fubini-Study metric Huang, Xiaojun Li, Song-Ying Complex Variables 32F45, 32Q30, 32E10, 53C25 Domains and more generally complex manifolds whose Bergman metrics have constant holomorphic sectional curvature are characterized. Our approach is to treat the Bergman metrics as the pull-back by the Bergman-Bochner maps of the Fubini-Study metric of the complex projective space of infinite dimension. Several new domains with surprising curvature properties for their Bergman metrics are constructed. A new conjecture is also formulated at the end of the paper. |
| title | Bergman metrics as pull-backs of the Fubini-Study metric |
| topic | Complex Variables 32F45, 32Q30, 32E10, 53C25 |
| url | https://arxiv.org/abs/2302.13456 |