@article {2013,
title = {Curved noncommutative torus and Gauss--Bonnet},
journal = {Journal of Mathematical Physics. Volume 54, Issue 1, 22 January 2013, Article number 013518},
number = {arXiv:1204.0420v1;},
year = {2013},
note = {The article is composed of 13 pages and is recorded in PDF format},
publisher = {American Institute of Physics},
abstract = {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.},
keywords = {Geometry},
doi = {10.1063/1.4776202},
url = {http://hdl.handle.net/1963/7376},
author = {Ludwik Dabrowski and Andrzej Sitarz}
}