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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.14007 |
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| _version_ | 1866914323535757312 |
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| author | Fang, Hao Jordan, Joshua |
| author_facet | Fang, Hao Jordan, Joshua |
| contents | In this paper, we study bi-Hermitian metrics on complex surfaces with split holomorphic tangent bundle and construct 2 types of metric cones. We introduce a new type of fully non-linear geometric PDE on such surfaces and establish smooth solutions. As a geometric application, we solve the prescribed Bismut Ricci problem. In various settings, we obtain canonical metrics on 2 important classes of complex surfaces: primary Hopf surfaces and Inoue surfaces of type $\mathcal{S}_{M}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14007 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On canonical metrics of complex surfaces with split tangent and related geometric PDEs Fang, Hao Jordan, Joshua Differential Geometry 53C55 In this paper, we study bi-Hermitian metrics on complex surfaces with split holomorphic tangent bundle and construct 2 types of metric cones. We introduce a new type of fully non-linear geometric PDE on such surfaces and establish smooth solutions. As a geometric application, we solve the prescribed Bismut Ricci problem. In various settings, we obtain canonical metrics on 2 important classes of complex surfaces: primary Hopf surfaces and Inoue surfaces of type $\mathcal{S}_{M}$. |
| title | On canonical metrics of complex surfaces with split tangent and related geometric PDEs |
| topic | Differential Geometry 53C55 |
| url | https://arxiv.org/abs/2406.14007 |