00967nas a2200133 4500008004100000245005000041210004800091260003400139520056900173653001300742100002200755700002000777856003600797 2013 en d00aCurved noncommutative torus and Gauss--Bonnet0 aCurved noncommutative torus and GaussBonnet bAmerican Institute of Physics3 aWe study perturbations of the flat geometry of the noncommutative
two-dimensional torus T^2_\theta (with irrational \theta). They are described
by spectral triples (A_\theta, \H, D), with the Dirac operator D, which is a
differential operator with coefficients in the commutant of the (smooth)
algebra A_\theta of T_\theta. We show, up to the second order in perturbation,
that the zeta-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.10aGeometry1 aDabrowski, Ludwik1 aSitarz, Andrzej uhttp://hdl.handle.net/1963/7376