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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.20149 |
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| _version_ | 1866911262555766784 |
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| author | Zhu, Xuwen |
| author_facet | Zhu, Xuwen |
| contents | This note extends the construction of $D_{k}$ ALF gravitational instantons in Schroers--Singer to a new case where the nonlinear superposition is given by the $D_{1}$ Atiyah--Hitchin metric and $k-1$ copies of $A_{0}$ Taub-NUT metrics. We then give a general class of ALF spaces such that each of them contains a non-holomorphic minimal sphere. Together with Foscolo's construction this gives a large class of $K3$ surfaces containing non-holomorphic minimal spheres. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20149 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A gluing construction of $D_{k}$ ALF gravitational instantons and existence of non-holomorphic minimal spheres Zhu, Xuwen Differential Geometry Mathematical Physics This note extends the construction of $D_{k}$ ALF gravitational instantons in Schroers--Singer to a new case where the nonlinear superposition is given by the $D_{1}$ Atiyah--Hitchin metric and $k-1$ copies of $A_{0}$ Taub-NUT metrics. We then give a general class of ALF spaces such that each of them contains a non-holomorphic minimal sphere. Together with Foscolo's construction this gives a large class of $K3$ surfaces containing non-holomorphic minimal spheres. |
| title | A gluing construction of $D_{k}$ ALF gravitational instantons and existence of non-holomorphic minimal spheres |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2407.20149 |