@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} } @article {2013, title = {Some open problems}, number = {arXiv:1304.2590;}, year = {2013}, publisher = {SISSA}, abstract = {We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry.}, keywords = {Geometry}, url = {http://hdl.handle.net/1963/7070}, author = {Andrei A. Agrachev} }