Classification of closed conformally flat Lorentzian manifolds with unipotent holonomy

Fuente: arXiv
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Main Authors: Lee, Rachel, Melnick, Karin
Format: Preprint
Published: 2024
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author Lee, Rachel
Melnick, Karin
author_facet Lee, Rachel
Melnick, Karin
contents We classify closed, conformally flat Lorentzian manifolds of dimension $n \geq 3$ with unipotent holonomy in PO(2,n). They are all Kleinian and fall into four different geometric types according to the intersection of the image of the developing map with a holonomy-invariant isotropic flag. They are homeomorphic to $S^{n-1} \times S^1$ or a nilmanifold of degree at most three, up to a finite cover. We classify those admitting an essential conformal flow; these fall into two geometric types, both homeomorphic to $S^{n-1} \times S^1$ up to finite cover.
format Preprint
id arxiv_https___arxiv_org_abs_2405_08410
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Classification of closed conformally flat Lorentzian manifolds with unipotent holonomy
Lee, Rachel
Melnick, Karin
Differential Geometry
Geometric Topology
53C50, 57N16
We classify closed, conformally flat Lorentzian manifolds of dimension $n \geq 3$ with unipotent holonomy in PO(2,n). They are all Kleinian and fall into four different geometric types according to the intersection of the image of the developing map with a holonomy-invariant isotropic flag. They are homeomorphic to $S^{n-1} \times S^1$ or a nilmanifold of degree at most three, up to a finite cover. We classify those admitting an essential conformal flow; these fall into two geometric types, both homeomorphic to $S^{n-1} \times S^1$ up to finite cover.
title Classification of closed conformally flat Lorentzian manifolds with unipotent holonomy
topic Differential Geometry
Geometric Topology
53C50, 57N16
url https://arxiv.org/abs/2405.08410