Are there general results  about closed Semi-Riemannian manifolds which have a non-compact isometry group?

*Background:* By a theorem of Myers and Steenrod the isometry group of a Riemannian manifold is a lie group. The same is true for Semi-Riemannian manifolds where the idea of a possible proof (which also works for Riemannian manifolds) is to embed the isometry group into the bundle of orthonormal frames as a closed submanifold. In the case of Riemannian manifolds this immediately yields that the isometry group of a compact Riemannian manifold has to be compact. But this is in general false for Semi-Riemannian manifolds since the bundle of orthonormal frames is not necessarily compact in this case even if the manifold is. So I ask myself if there are general statements about the phenomenon of a closed Semi-Riemannian manifold with non-compact isometry group. One statement that I know of is about Lorentzian manifolds and goes as follows:

**Theorem:** Let $(M,g)$ be a closed, simply connected Lorentz manifold and assume $M$ and $g$ are analytic. Then the isometry group of $M$ is compact.