Conformally homogeneous Lorentzian spaces
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912570729824256 |
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| author | Alekseevsky, Dmitri V. Galaev, Anton S. |
| author_facet | Alekseevsky, Dmitri V. Galaev, Anton S. |
| contents | We prove that if a 1-connected non-conformally flat conformal Lorentzian manifold $(M,c)$ admits a connected essential transitive group of conformal transformations, then there exists a metric $g\in c$ such that $(M,g)$ is a complete homogeneous plane wave. This finishes the classification of 1-connected Lorentzian manifolds, which admit transitive essential conformal group. We also prove that the group of conformal transformations of a non-conformally flat 1-connected homogeneous plane wave $(M,g)$ consists of homotheties, and it is a 1-dimensional extension of the group of isometries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03095 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformally homogeneous Lorentzian spaces Alekseevsky, Dmitri V. Galaev, Anton S. Differential Geometry We prove that if a 1-connected non-conformally flat conformal Lorentzian manifold $(M,c)$ admits a connected essential transitive group of conformal transformations, then there exists a metric $g\in c$ such that $(M,g)$ is a complete homogeneous plane wave. This finishes the classification of 1-connected Lorentzian manifolds, which admit transitive essential conformal group. We also prove that the group of conformal transformations of a non-conformally flat 1-connected homogeneous plane wave $(M,g)$ consists of homotheties, and it is a 1-dimensional extension of the group of isometries. |
| title | Conformally homogeneous Lorentzian spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2407.03095 |