• DOI:10.3842/sigma.2020.143
• Corpus ID: 220302674

Riemannian Geometry of a Discretized Circle and Torus

@article{Bochniak2020RiemannianGO,
  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},
  year={2020}
}

• A. Bochniak, A. Sitarz, P. Zalecki
• Published 2 July 2020
• Mathematics
• 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 curvature for these metrics and find their continuous limits.