On Noncommutative Levi-Civita Connections
Operator Algebras
2018-01-11 v2
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.
Keywords
Cite
@article{arxiv.1511.02901,
title = {On Noncommutative Levi-Civita Connections},
author = {Mira A. Peterka and Albert J. L. Sheu},
journal= {arXiv preprint arXiv:1511.02901},
year = {2018}
}