general relativity - Is there a simply classification of maximally symmetric spaces?

By maximally symmetric space I mean a (pseudo-) Riemannian manifold of dimension $n$ that has $n(n+1)/2$ linearly independent Killing vector fields. I seem to remember that there are only three kinds, one of them being Minkowski space, and another being de Sitter space. And the third probably being the sphere. But I'm not quite sure this is true in any dimension. Can someone shed some light on this issue? I would also very much appreciate references.

EDIT: Although the question above might have suggested it (because I wasn't thinking straight), I do not mean to focus on Lorentzian manifolds only. Indeed, as mentioned in the comments, the sphere I mention above is Riemannian, while the other two mentioned manifolds are Lorentzian, so that did not make very much sense on my part, because clearly there are more geometries then three (in at least 2 dimensions), thinking of Euclidean space.