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arXiv · 1511.02901

On Noncommutative Levi-Civita Connections

Mira A. Peterka·Albert J. L. Sheu
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Abstract

We make some observations about Rosenberg's Levi-Civita connections on noncommutative tori, noting the non-uniqueness of torsion-free metric-compatible connections without prescribed connection operator for the inner *-derivations, the nontrivial curvature form of the inner *-derivations, and the validity of the Gauss-Bonnet theorem for two classes of non-conformal deformations of the flat metric on the noncommutative two-tori, including the case of non-commuting scalings along the principal directions of a two-torus.

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Mira A. Peterka, Albert J. L. Sheu. 2016-10-27. On Noncommutative Levi-Civita Connections. https://doi.org/10.1142/s0219887817500712

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