We solve for quantum Riemannian geometries on the finite lattice interval • - • -⋯- • with n nodes (the Dynkin graph of type An) and find that they are necessarily q-deformed with q = e ı π n + 1 . This comes out of the ...

Following steps analogous to classical Kaluza-Klein theory, we solve for the quantum Riemannian geometry on C∞(M) ⊗ M 2(ℂ) in terms of classical Riemannian geometry on a smooth manifold M , a finite quantum geometry on the ...

We study geodesics flows on curved quantum Riemannian geometries using a recent formulation in terms of bimodule connections and completely positive maps. We complete this formalism with a canonical operation on ...