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 -