%0 Journal Article
%J Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518
%D 2013
%T Curved noncommutative torus and Gauss--Bonnet
%A Ludwik Dabrowski
%A Andrzej Sitarz
%K Geometry
%X We 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.
%B Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518
%I American Institute of Physics
%G en
%U http://hdl.handle.net/1963/7376
%1 7424
%2 Mathematics
%4 1
%# MAT/07 FISICA MATEMATICA
%$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2014-06-17T13:10:21Z
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%R 10.1063/1.4776202