Riemannian Geometry of a Discretized Circle and Torus

  title={Riemannian Geometry of a Discretized Circle and Torus},
  author={Arkadiusz Bochniak and Andrzej Sitarz and P. Zalecki},
  journal={Symmetry, Integrability and Geometry: Methods and Applications},
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∗-module structure on the space of the one-forms. We compute curvature and scalar… 

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