Conformal quotients of plane waves, and Lichnerowicz conjecture in a locally homogeneous setting
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913730348974080 |
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| author | Mehidi, Lilia |
| author_facet | Mehidi, Lilia |
| contents | In the first part of the paper, we study conformal groups that act properly discontinuously and cocompactly on simply connected, non-flat homogeneous plane waves. We show that proper cocompact similarity actions that are not isometric can occur, in contrast to the behavior of Riemannian and Lorentzian affine similarity actions. In the second part, we consider the Lorentzian conformal Lichnerowicz conjecture, which states that if the conformal group of a compact Lorentzian manifold acts without preserving any metric in the conformal class, then the manifold must be conformally flat. We prove the conjecture in a locally homogeneous setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08614 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformal quotients of plane waves, and Lichnerowicz conjecture in a locally homogeneous setting Mehidi, Lilia Differential Geometry 53C50, 53B30 In the first part of the paper, we study conformal groups that act properly discontinuously and cocompactly on simply connected, non-flat homogeneous plane waves. We show that proper cocompact similarity actions that are not isometric can occur, in contrast to the behavior of Riemannian and Lorentzian affine similarity actions. In the second part, we consider the Lorentzian conformal Lichnerowicz conjecture, which states that if the conformal group of a compact Lorentzian manifold acts without preserving any metric in the conformal class, then the manifold must be conformally flat. We prove the conjecture in a locally homogeneous setting. |
| title | Conformal quotients of plane waves, and Lichnerowicz conjecture in a locally homogeneous setting |
| topic | Differential Geometry 53C50, 53B30 |
| url | https://arxiv.org/abs/2503.08614 |