Riemannian Geometry of a Discretized Circle and Torus
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
| ISSN: | 1815-0659 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211076 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Riemannian Geometry of a Discretized Circle and Torus. Arkadiusz Bochniak, Andrzej Sitarz and Paweł Zalecki. SIGMA 16 (2020), 143, 28 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 *-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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| ISSN: | 1815-0659 |