Levi-Civita's Theorem for Noncommutative Tori

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2013
• 1. Verfasser: Rosenberg, J.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2013
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/149363
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Levi-Civita's Theorem for Noncommutative Tori / L. Rosenberg // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 11 назв. — англ.

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...