TY - JOUR T1 - Curved noncommutative torus and Gauss--Bonnet JF - Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518 Y1 - 2013 A1 - Ludwik Dabrowski A1 - Andrzej Sitarz KW - Geometry AB - 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. PB - American Institute of Physics UR - http://hdl.handle.net/1963/7376 N1 - The article is composed of 13 pages and is recorded in PDF format U1 - 7424 U2 - Mathematics U4 - 1 U5 - MAT/07 FISICA MATEMATICA ER -