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On Noncommutative Levi-Civita Connections

By Mira A. Peterka and Albert J. L. Sheu

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

Topics: Mathematics - Operator Algebras, 46L87, 58B34, 46L08
Publisher: 'World Scientific Pub Co Pte Lt'
Year: 2016
DOI identifier: 10.1142/S0219887817500712
OAI identifier: oai:arXiv.org:1511.02901

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