Is Minkowski spacetime a solution of the Friedmann Equations?

[Orodruin]

This is consistent with the result you mention that the different 2d manifold of constant negative curvature cannot be fully embedded in Euclidean 3 space (smoothly, isometrically).

I think it should be stressed that that manifold is a hyperbolic space, not a hyperboloid. These are not the same thing.