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Levi-Civita's Theorem for Noncommutative Tori
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2013, том 9
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Levi-Civita's Theorem for Noncommutative Tori
Інший ID:
2010 Mathematics Subject Classification: 46L87; 58B34; 46L08; 46L08
DOI: http://dx.doi.org/10.3842/SIGMA.2013.071
DOI: http://dx.doi.org/10.3842/SIGMA.2013.071
Посилання:
Levi-Civita's Theorem for Noncommutative Tori / L. Rosenberg // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 11 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in
honor of Marc A. Rief fel. The full collection is available at http://www.emis.de/journals/SIGMA/Rieffel.html.
This research was supported by NSF grant DMS-1206159. The author thanks the referees and
the participants at the Fields Institute Focus Program for several interesting comments and
discussions. I would like to thank Joakim Arnlind for pointing out a mistake in the original
formulation of Proposition 3.4
Дата:
2013
Переглядів:
476
Завантажень:
241
Анотація:
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.
