We study perturbations of the flat geometry of the noncommutative two-dimensional torus (with irrational θ). They are described by spectral triples , with the Dirac operator D, which is a differential operator with coefficients in the commutant of the (smooth) algebra Aθ of . We show, up to the second order in perturbation, that the ζ-function at 0 vanishes and so the Gauss-Bonnet theorem holds. We also calculate first two terms of the perturbative expansion of the corresponding local scalar curvature.
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2013
American Institute of Physics
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