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arXiv · 1307.3775

Levi-Civita's Theorem for Noncommutative Tori

Jonathan Rosenberg
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Abstract

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.

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Jonathan Rosenberg. 2015-01-20. Levi-Civita's Theorem for Noncommutative Tori. https://doi.org/10.3842/sigma.2013.071

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