  We characterize the universal covering of connected analytic
pseudo-Riemannian manifolds which admit a non-trivial and isometric action of
the simple Lie group $SL(3,\mathbb{R})$ with a dense orbit preserving a finite
volume. If such manifold is also weakly irreducible we prove that $M$ is
isometric to, or a quotient space of, a simple Lie group containing
$SL(3,\mathbb{R})$.
