Levi-Civita's Theorem for Noncommutative Tori

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2013
• Автор: Rosenberg, J.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2013
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/149363
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: 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...