The complex hyperbolic form as a Weil-Petersson form
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916228593876992 |
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| author | Wang, Xiangsheng |
| author_facet | Wang, Xiangsheng |
| contents | For the moduli space of the punctured spheres, we find a new equality between two symplectic forms defined on it. Namely, by treating the elements of this moduli space as the singular Euclidean metrics on a sphere, we give an interpretation of the complex hyperbolic form, i.e. the Kähler form of the complex hyperbolic structure on the moduli space, as a kind of Weil-Petersson form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_10842 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The complex hyperbolic form as a Weil-Petersson form Wang, Xiangsheng Differential Geometry Geometric Topology 57M50, 32G15, 58G30, 58F05 For the moduli space of the punctured spheres, we find a new equality between two symplectic forms defined on it. Namely, by treating the elements of this moduli space as the singular Euclidean metrics on a sphere, we give an interpretation of the complex hyperbolic form, i.e. the Kähler form of the complex hyperbolic structure on the moduli space, as a kind of Weil-Petersson form. |
| title | The complex hyperbolic form as a Weil-Petersson form |
| topic | Differential Geometry Geometric Topology 57M50, 32G15, 58G30, 58F05 |
| url | https://arxiv.org/abs/2209.10842 |