Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917875834421248 |
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| author | Borthwick, Jack Herfray, Yannick |
| author_facet | Borthwick, Jack Herfray, Yannick |
| contents | In this article we discuss how to construct canonical \emph{strong} Carrollian geometries at time/space like infinity of projectively compact Ricci flat Einstein manifolds $(M,g)$ and discuss the links between the underlying projective structure of the metric $g$. The obtained Carrollian geometries are determined by the data of the projective compactification. The key idea to achieve this is to consider a new type of Cartan geometry based on a non-effective homogeneous model for projective geometry. We prove that this structure is a general feature of projectively compact Ricci flat Einstein manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01800 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds Borthwick, Jack Herfray, Yannick Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics In this article we discuss how to construct canonical \emph{strong} Carrollian geometries at time/space like infinity of projectively compact Ricci flat Einstein manifolds $(M,g)$ and discuss the links between the underlying projective structure of the metric $g$. The obtained Carrollian geometries are determined by the data of the projective compactification. The key idea to achieve this is to consider a new type of Cartan geometry based on a non-effective homogeneous model for projective geometry. We prove that this structure is a general feature of projectively compact Ricci flat Einstein manifolds. |
| title | Projective and Carrollian geometry at time/space-like infinity on projectively compact Ricci flat Einstein manifolds |
| topic | Differential Geometry General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2406.01800 |