Comptes Rendus
Group theory/Differential geometry
On the irreducible action of PSL(2,R) on the 3-dimensional Einstein universe
[Sur l'action irréductible de PSL(2,R) sur l'univers d'Einstein de dimension 3]
Comptes Rendus. Mathématique, Volume 355 (2017) no. 11, pp. 1133-1137.

Dans cet article, nous étudions l'action irréductible de PSL(2,R) dans PSL(5,R). Cette action préserve une forme quadratique de signature (2,3). Elle sur agit donc conformément sur l'univers d'Einstein Ein1,2 de dimension 3, ainsi que sur son complément dans RP4. Ce travail complète l'étude préliminaire dans [2], et est un élément de la classification des actions sur Ein1,2 de cohomogenéité un [5].

In this paper, we study the irreducible representation of PSL(2,R) in PSL(5,R). This action preserves a quadratic form with signature (2,3). Thus, it acts conformally on the 3-dimensional Einstein universe Ein1,2. We describe the orbits induced in Ein1,2 and its complement in RP4. This work completes the study in [2], and is one element of the classification of cohomogeneity one actions on Ein1,2 [5].

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.10.003

Masoud Hassani 1, 2

1 Université d'Avignon, Campus Jean-Henri-Fabre, 301, rue Baruch-de-Spinoza, BP 21239, 84916 Avignon cedex 9, France
2 University of Zanjan, Faculty of Science, Department of Mathematics, University blvd, Zanjan, Iran
@article{CRMATH_2017__355_11_1133_0,
     author = {Masoud Hassani},
     title = {On the irreducible action of $ \text{PSL}(2,\mathbb{R})$ on the 3-dimensional {Einstein} universe},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1133--1137},
     publisher = {Elsevier},
     volume = {355},
     number = {11},
     year = {2017},
     doi = {10.1016/j.crma.2017.10.003},
     language = {en},
}
TY  - JOUR
AU  - Masoud Hassani
TI  - On the irreducible action of $ \text{PSL}(2,\mathbb{R})$ on the 3-dimensional Einstein universe
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 1133
EP  - 1137
VL  - 355
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crma.2017.10.003
LA  - en
ID  - CRMATH_2017__355_11_1133_0
ER  - 
%0 Journal Article
%A Masoud Hassani
%T On the irreducible action of $ \text{PSL}(2,\mathbb{R})$ on the 3-dimensional Einstein universe
%J Comptes Rendus. Mathématique
%D 2017
%P 1133-1137
%V 355
%N 11
%I Elsevier
%R 10.1016/j.crma.2017.10.003
%G en
%F CRMATH_2017__355_11_1133_0
Masoud Hassani. On the irreducible action of $ \text{PSL}(2,\mathbb{R})$ on the 3-dimensional Einstein universe. Comptes Rendus. Mathématique, Volume 355 (2017) no. 11, pp. 1133-1137. doi : 10.1016/j.crma.2017.10.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.10.003/

[1] T. Barbot; V. Charette; T. Drumm; W.M. Goldman; K. Melnick A primer on the (2+1) Einstein universe (D.V. Alekseevsky; H. Baum, eds.), Recent Developments in Pseudo-Riemannian Geometry, ESI Lectures in Mathematics and Physics, 2008, pp. 179-229

[2] B. Collier; N. Tholozan; J. Toulisse The geometry of maximal representations of surface groups into SO(2,n) | arXiv

[3] A.J. Di Scala; T. Leistner Connected subgroups of SO(2,n) acting irreducibly on R2,n, Isr. J. Math., Volume 182 (2011), pp. 103-122

[4] C. Frances Géometrie et dynamique lorentziennes conformes, ENS Lyon, France, 2002 (PhD thesis)

[5] M. Hassani, Cohomogeneity one actions on the three-dimensional Einstein universe, in preparation.

Cité par Sources :

This work is funded by the French Ministry of Foreign Affairs, through Campus France. Grant number 878286E. It is also part of project MATH AMSUD 2017, Project No. 38888QB – GDAR.

Commentaires - Politique