Gauss-Bonnet formula for metrics with logarithmic singularities on compact Riemann surfaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866916878130085888 |
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| author | Lyu, Yuanjiu Xu, Bin |
| author_facet | Lyu, Yuanjiu Xu, Bin |
| contents | We prove a generalization of the classical Gauss-Bonnet formula for metrics with logarithmic singularities on compact Riemann surfaces, under the condition that the Gaussian curvature is Lebesgue integrable with respect to the metric's area form. As an application, we establish the Gauss-Bonnet formula for special Kähler metrics when their associated cubic differentials are meromorphic on compact Riemann surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01632 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gauss-Bonnet formula for metrics with logarithmic singularities on compact Riemann surfaces Lyu, Yuanjiu Xu, Bin Differential Geometry 53C21, 14H15 53C21, 14H15 53C21, 14H15 53C21, 14H15 We prove a generalization of the classical Gauss-Bonnet formula for metrics with logarithmic singularities on compact Riemann surfaces, under the condition that the Gaussian curvature is Lebesgue integrable with respect to the metric's area form. As an application, we establish the Gauss-Bonnet formula for special Kähler metrics when their associated cubic differentials are meromorphic on compact Riemann surfaces. |
| title | Gauss-Bonnet formula for metrics with logarithmic singularities on compact Riemann surfaces |
| topic | Differential Geometry 53C21, 14H15 53C21, 14H15 53C21, 14H15 53C21, 14H15 |
| url | https://arxiv.org/abs/2508.01632 |