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Pré-Publication, Document De Travail Année : 2023

Topology and Dynamics of compact plane waves

Résumé

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.

Dates et versions

hal-04271797 , version 1 (06-11-2023)

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Malek Hanounah, Ines Kath, Lilia Mehidi, Abdelghani Zeghib. Topology and Dynamics of compact plane waves. 2023. ⟨hal-04271797⟩
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