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Journal of Lie Theory 27 (2017), No. 4, 1179--1197
Copyright Heldermann Verlag 2017

Rigidity of an Isometric SL(3,R)-Action

Raúl Quiroga-Barranco
CIMAT, Apartado Postal 402, Guanajuato 36250, Mexico

Eli Roblero-Méndez
Universidad Autónoma de Chiapas, Carretera Emiliano Zapata Km 8, Tuxtla Gutierrez 29050, Chiapas -- Mexico

We describe the universal covering space of a finite volume connected analytic pseudo-Riemannian manifold M with dimension at most 14 that admits a non-trivial isometric analytic action of the simple Lie group SL(3,R) with a dense orbit. If such a manifold is also weakly irreducible we prove that M-tilde is isometric to, or a quotient space of a simple Lie group containing SL(3,R).

Keywords: Simple Lie groups, pseudo-Riemannian manifolds, rigidity results.

MSC: 22F50, 53C24, 53C50

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