Topology and Dynamics of compact plane waves
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912121251430400 |
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| author | Hanounah, Malek Kath, Ines Mehidi, Lilia Zeghib, Abdelghani |
| author_facet | Hanounah, Malek Kath, Ines Mehidi, Lilia Zeghib, Abdelghani |
| contents | We study compact locally homogeneous plane waves. Such a manifold is a quotient of a homogeneous plane wave $X$ by a discrete subgroup of its isometry group. This quotient is called standard if the discrete subgroup is contained in a connected subgroup of the isometry group that acts properly cocompactly on $X$. We show that compact quotients of homogeneous plane waves are ``essentially" standard; more precisely, we show that they are standard or `semi-standard'. We find conditions which ensure that a quotient is not only semi-standard but even standard. As a consequence of these results, we obtain that the flow of the parallel isotropic vector field of a compact locally homogeneous plane wave is equicontinuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_14955 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topology and Dynamics of compact plane waves Hanounah, Malek Kath, Ines Mehidi, Lilia Zeghib, Abdelghani Differential Geometry 53C50, 53B30 We study compact locally homogeneous plane waves. Such a manifold is a quotient of a homogeneous plane wave $X$ by a discrete subgroup of its isometry group. This quotient is called standard if the discrete subgroup is contained in a connected subgroup of the isometry group that acts properly cocompactly on $X$. We show that compact quotients of homogeneous plane waves are ``essentially" standard; more precisely, we show that they are standard or `semi-standard'. We find conditions which ensure that a quotient is not only semi-standard but even standard. As a consequence of these results, we obtain that the flow of the parallel isotropic vector field of a compact locally homogeneous plane wave is equicontinuous. |
| title | Topology and Dynamics of compact plane waves |
| topic | Differential Geometry 53C50, 53B30 |
| url | https://arxiv.org/abs/2309.14955 |