....."In this case, geometrically speaking, space-time turns from a Riemannian..."
In regards to the above I say-----i.e. positive shaped ( ) curved { geodesic } space
......"space envisaged by the General Relativity (GR) into a generalized affine - metrical space. Respective gravitational field equations that generalize Einstein's equations show that torsion and nonmetricity can also spread in the form of waves (in particular plane waves at a great distance from wave sources).".........
Plane waves? A plane is 2D ex triangle or square plane polygons define a planes area. So not yet sure what "plane waves" is exactly. I envision them meaning that we take for example, a quasi-wave-linear, 2D sine-wave ---peaks and troughs /\/\/\/--- and are able to express that information on a 2D plane ergo no peaks and troughs but still some kind of torsion i.e. to me this means the plane is twisted yet still plane-like.
Here is possible approximation of what their math does not give an image of. Again, I'm certainly no mathematician and people likes us need a visual to make sense so what a mathematician is saying, with complex non visual maths.
Or a twisted plane? Does that mean both positive and negative curvature?
Mobieus? Torus?
The cubo{6}-octa{8}hedron via Fullers jitterbug;
1} contracts-expands,
2} torques/twists,
3} spins,
4} inside-outs,
5} has positive ( ) convex shape, and,
6} transforms into negative )( concave shape aka saddle shape,
7} a 2D wave plane i.e. rippled { peaks and troughs } complex octagon,
8} hexagonal 2D plane with perpendicular triangular tail wing ergo __/\
9} 2D set of four triangles ---double-valenced/bonded,
10} single triangle ---octa-valenced/bonded set of triangles---