# 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 CAT(-1) space or a quasi-tree.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-02006189
Contributor : Thomas Haettel <>
Submitted on : Monday, February 4, 2019 - 2:36:33 PM
Last modification on : Monday, February 10, 2020 - 6:13:49 PM

### Identifiers

• HAL Id : hal-02006189, version 1
• ARXIV : 1901.07462

### Citation

Indira Chatterji, François Dahmani, Thomas Haettel, Jean Lecureux. Tangent bundles of hyperbolic spaces and proper affine actions on $L^p$ spaces. 2019. ⟨hal-02006189⟩

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