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arXiv · 2007.01241

Riemannian Geometry of a Discretized Circle and Torus

Arkadiusz Bochniak·Andrzej Sitarz·Paweł Zalecki
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Abstract

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.

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Arkadiusz Bochniak, Andrzej Sitarz, Paweł Zalecki. 2020-07-02. Riemannian Geometry of a Discretized Circle and Torus. https://doi.org/10.3842/sigma.2020.143

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