Geodesic
Riemannian Geometry of a Discretized Circle and Torus
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: noncommutative Riemannian geometry, linear connections, curvature. 
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     author = {Arkadiusz Bochniak and Andrzej Sitarz and Pawel{\l} Zalecki},
     title = {Riemannian {Geometry} of a {Discretized} {Circle} and {Torus}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2020},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a142/}
}
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Arkadiusz Bochniak; Andrzej Sitarz; Pawelł Zalecki. Riemannian Geometry of a Discretized Circle and Torus. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a142/

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