Tangent bundles of hyperbolic spaces and proper affine actions on $L^p$ spaces
Abstract
We define the notion of a negatively curved tangent bundle of a metric measured space. We prove that, when a group $G$ acts on a metric measured space $X$ with a negatively curved tangent bundle, then $G$ acts on some $L^p$ space, and that this action is proper under suitable assumptions. We then check that this result applies to the case when $X$ is a hyperbolic space.
 Publication:

arXiv eprints
 Pub Date:
 January 2019
 DOI:
 10.48550/arXiv.1901.07462
 arXiv:
 arXiv:1901.07462
 Bibcode:
 2019arXiv190107462C
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Metric Geometry