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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.12323 |
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| _version_ | 1866912023121494016 |
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| author | Ganguly, Soumya Sinha, Shubham |
| author_facet | Ganguly, Soumya Sinha, Shubham |
| contents | We show that the Bergman metric of the ball quotients $\mathbb{B}^2/Γ$, where $Γ$ is a finite and fixed point free group, is Kähler-Einstein if and only if $Γ$ is trivial. As a consequence, we characterize the unit ball $\mathbb{B}^2$, among 2 dimensional Stein spaces with isolated normal singularities, proving an algebraic version of Cheng's conjecture for 2 dimensional Stein spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_12323 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Bergman-Einstein metrics on two-dimensional Stein spaces Ganguly, Soumya Sinha, Shubham Complex Variables Metric Geometry 32Q20 (Primary), 32V20, 32C15, 32M18 We show that the Bergman metric of the ball quotients $\mathbb{B}^2/Γ$, where $Γ$ is a finite and fixed point free group, is Kähler-Einstein if and only if $Γ$ is trivial. As a consequence, we characterize the unit ball $\mathbb{B}^2$, among 2 dimensional Stein spaces with isolated normal singularities, proving an algebraic version of Cheng's conjecture for 2 dimensional Stein spaces. |
| title | Bergman-Einstein metrics on two-dimensional Stein spaces |
| topic | Complex Variables Metric Geometry 32Q20 (Primary), 32V20, 32C15, 32M18 |
| url | https://arxiv.org/abs/2210.12323 |