# The identity component of the isometry group of a compact Lorentz manifold

@article{Zeghib1998TheIC, title={The identity component of the isometry group of a compact Lorentz manifold}, author={Abdelghani Zeghib}, journal={Duke Mathematical Journal}, year={1998}, volume={92}, pages={321-333} }

This result may be compared with a Theorem of E. Ghys [Ghy] (see also [Bel]), asserting a similar conclusion, but assuming that M has dimension 3, and that the action is just volume preserving and locally free. The statement there, is that the action of AG may be extended to an action of a finite cover of PSL(2,R), or to an action of the solvable 3-dimensional Lie group SOL. Here we have another motivation. We want to understand the structure of Lie groups acting isometrically on compact…

## 47 Citations

Lorentzian manifolds with a conformal action of SL(2,R)

- MathematicsCommentarii Mathematici Helvetici
- 2018

We consider conformal actions of simple Lie groups on compact Lorentzian manifolds. Mainly motivated by the Lorentzian version of a conjecture of Lichnerowicz, we establish the alternative: Either…

Dynamics on Lorentz manifolds ENSET Oran , November 4-9 , 2006

- Mathematics
- 2009

This course was given at ENSET Oran, November 4-9, 2006. It is an introduction to isometric actions of Lie groups on Lorentz manifolds. Several examples are presented, followed by general definitions…

Ja n 20 05 Isometric actions of Heisenberg groups on compact Lorentz manifolds January 14 , 2004

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Connected isometry groups of compact connected Lorentz manifolds have been classified by Adams and Stuck and independently by Zeghib. The identity component of the isometry group of a compact…

Isometry groups of Lorentzian manifolds of finite volume

- Mathematics
- 2011

Based on the work of Adams and Stuck as well as on the work of Zeghib, we classify the Lie groups which can act isometrically and locally effectively on Lorentzian manifolds of finite volume. In the…

Isometry group of Lorentz manifolds: A coarse perspective

- MathematicsGeometric and Functional Analysis
- 2021

— We prove a structure theorem for the isometry group Iso(M, g) of a compact Lorentz manifold, under the assumption that a closed subgroup has exponential growth. We don’t assume anything about the…

Transitive Actions on Lorentz Manifolds with Noncompact Stabilizer

- Mathematics
- 2003

If a topological group G acts on a topological space X, then we say that the action is orbit nonproper provided that, for some x ∈ X, the orbit map g↦gx:G → X is nonproper. We consider the problem of…

On the affine group of a normal homogeneous manifold

- Mathematics
- 2010

A very important class of homogeneous Riemannian manifolds are the so-called normal homogeneous spaces, which have associated a canonical connection. In this study, we obtain geometrically the…

Essential conformal actions of PSL(2,R) on real-analytic compact Lorentz manifolds

- Mathematics
- 2015

The main result of this paper is the conformal flatness of real-analytic compact Lorentz manifolds of dimension at least $3$ admitting a conformal essential (i.e. conformal, but not isometric) action…

Naturally reductive Riemannian manifolds

- Mathematics
- 2009

A very important class of homogeneous Riemannian manifolds are the so-called normal homogeneous spaces, which have associated a canonical connection. In this work we obtain geometrically the…

Compact Lorentz manifolds with local symmetry

- Mathematics
- 2006

We prove a structure theorem for compact aspherical Lorentz manifolds with abundant local symmetry. If M is a compact, aspherical, real-analytic, complete Lorentz manifold such that the isometry…

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