Local Rigidity of the Bergman Metric and of the Kähler Carathéodory Metric
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918462317658112 |
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| author | Dong, Robert Xin Wang, Ruoyi Wong, Bun |
| author_facet | Dong, Robert Xin Wang, Ruoyi Wong, Bun |
| contents | We prove that if the Carathéodory metric on a strictly pseudoconvex domain with a smooth boundary is locally Kähler near the boundary, then the domain is biholomorphic to a ball. We also establish a local rigidity theorem for domains with Bergman metrics of constant holomorphic sectional curvature, and highlight this relationship with the Lu constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09572 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local Rigidity of the Bergman Metric and of the Kähler Carathéodory Metric Dong, Robert Xin Wang, Ruoyi Wong, Bun Complex Variables Differential Geometry Primary 32F45, Secondary 32T15, 32H02 We prove that if the Carathéodory metric on a strictly pseudoconvex domain with a smooth boundary is locally Kähler near the boundary, then the domain is biholomorphic to a ball. We also establish a local rigidity theorem for domains with Bergman metrics of constant holomorphic sectional curvature, and highlight this relationship with the Lu constant. |
| title | Local Rigidity of the Bergman Metric and of the Kähler Carathéodory Metric |
| topic | Complex Variables Differential Geometry Primary 32F45, Secondary 32T15, 32H02 |
| url | https://arxiv.org/abs/2408.09572 |