Einstein Structure of Four-Manifolds
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913981088661504 |
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| author | Ho, Jeongwon Kim, Kyung Kiu Yang, Hyun Seok |
| author_facet | Ho, Jeongwon Kim, Kyung Kiu Yang, Hyun Seok |
| contents | It is known that the moduli space of Einstein structures in four dimensions is generally considered to be rigid so that Einstein metrics tend to be isolated modulo diffeomorphisms under infinitesimal Einstein deformations. We examine the rigidity of the Einstein structure by considering deformations of the round four-sphere. We show that any deviation from the standard metric of the round four-sphere (except for scaling) breaks the Einstein condition. This further supports the idea of rigidity. We analyze the Einstein structure of four-manifolds based on the irreducible decomposition of the self-dual structure of Einstein manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05335 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Einstein Structure of Four-Manifolds Ho, Jeongwon Kim, Kyung Kiu Yang, Hyun Seok Differential Geometry High Energy Physics - Theory Mathematical Physics It is known that the moduli space of Einstein structures in four dimensions is generally considered to be rigid so that Einstein metrics tend to be isolated modulo diffeomorphisms under infinitesimal Einstein deformations. We examine the rigidity of the Einstein structure by considering deformations of the round four-sphere. We show that any deviation from the standard metric of the round four-sphere (except for scaling) breaks the Einstein condition. This further supports the idea of rigidity. We analyze the Einstein structure of four-manifolds based on the irreducible decomposition of the self-dual structure of Einstein manifolds. |
| title | Einstein Structure of Four-Manifolds |
| topic | Differential Geometry High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2309.05335 |