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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2209.04814 |
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| _version_ | 1866912547516448768 |
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| author | Lye, Jørgen Olsen |
| author_facet | Lye, Jørgen Olsen |
| contents | This article studies Kummer K3 surfaces close to the orbifold limit. We improve upon estimates for the Calabi-Yau metrics due to R. Kobayashi. As an application, we study stable closed geodesics. We use the metric estimates to show how there are generally restrictions on the existence of such geodesics. We also show how there can exist stable, closed geodesics in some highly symmetric circumstances due to hyperkähler identities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_04814 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Geodesics on a K3 Surface near the Orbifold Limit Lye, Jørgen Olsen Differential Geometry 53C21, 53C22, 53C26 This article studies Kummer K3 surfaces close to the orbifold limit. We improve upon estimates for the Calabi-Yau metrics due to R. Kobayashi. As an application, we study stable closed geodesics. We use the metric estimates to show how there are generally restrictions on the existence of such geodesics. We also show how there can exist stable, closed geodesics in some highly symmetric circumstances due to hyperkähler identities. |
| title | Geodesics on a K3 Surface near the Orbifold Limit |
| topic | Differential Geometry 53C21, 53C22, 53C26 |
| url | https://arxiv.org/abs/2209.04814 |