Levi-Civita's Theorem for Noncommutative Tori
We show how to define Riemannian metrics and connections on a noncommutative torus in such a way that an analogue of Levi-Civita's theorem on the existence and uniqueness of a Riemannian connection holds. The major novelty is that we need to use two different notions of noncommutative vector fi...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2013 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149363 |
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| Цитувати: | Levi-Civita's Theorem for Noncommutative Tori / L. Rosenberg // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 11 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149363 |
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dspace |
| spelling |
irk-123456789-1493632019-02-22T01:23:22Z Levi-Civita's Theorem for Noncommutative Tori Rosenberg, J. We show how to define Riemannian metrics and connections on a noncommutative torus in such a way that an analogue of Levi-Civita's theorem on the existence and uniqueness of a Riemannian connection holds. The major novelty is that we need to use two different notions of noncommutative vector field. Levi-Civita's theorem makes it possible to define Riemannian curvature using the usual formulas. 2013 Article Levi-Civita's Theorem for Noncommutative Tori / L. Rosenberg // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 11 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 46L87; 58B34; 46L08; 46L08 DOI: http://dx.doi.org/10.3842/SIGMA.2013.071 http://dspace.nbuv.gov.ua/handle/123456789/149363 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We show how to define Riemannian metrics and connections on a noncommutative torus in such a way that an analogue of Levi-Civita's theorem on the existence and uniqueness of a Riemannian connection holds. The major novelty is that we need to use two different notions of noncommutative vector field. Levi-Civita's theorem makes it possible to define Riemannian curvature using the usual formulas. |
| format |
Article |
| author |
Rosenberg, J. |
| spellingShingle |
Rosenberg, J. Levi-Civita's Theorem for Noncommutative Tori Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Rosenberg, J. |
| author_sort |
Rosenberg, J. |
| title |
Levi-Civita's Theorem for Noncommutative Tori |
| title_short |
Levi-Civita's Theorem for Noncommutative Tori |
| title_full |
Levi-Civita's Theorem for Noncommutative Tori |
| title_fullStr |
Levi-Civita's Theorem for Noncommutative Tori |
| title_full_unstemmed |
Levi-Civita's Theorem for Noncommutative Tori |
| title_sort |
levi-civita's theorem for noncommutative tori |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149363 |
| citation_txt |
Levi-Civita's Theorem for Noncommutative Tori / L. Rosenberg // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 11 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT rosenbergj levicivitastheoremfornoncommutativetori |
| first_indexed |
2023-05-20T17:32:49Z |
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2023-05-20T17:32:49Z |
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1796153537121484800 |