Curvature of Flat Lorentz manifolds

[RockyMarciano]

I like your idea that the Riemannian metric on the flat Lorentz manifold can be chosen to have a very uniform curvature tensor. Constant sectional curvature doesn't work but one would suspect that something very uniform does work.

Very benevolent of you.

 

[RockyMarciano]

@lavinia, would Minkowski space itself, for the timelike vector case(where the Lorentz group acts on the interior of the future timelike oriented cone) not have the same issue with its Lorentz isometries acting properly discontinuously and not being a subgroup of rigid euclidean motions?