  We extend the results of Riemannian geometry over finite groups and provide a
full classification of all linear connections for the minimal noncommutative
differential calculus over a finite cyclic group. We solve the torsion-free and
metric compatibility condition in general and show that there are several
classes of solutions, out of which only special ones are compatible with a
metric that gives a Hilbert $C^\ast$-module structure on the space of the
one-forms. We compute curvature and scalar curvature for these metrics and find
their continuous limits.
