An Asymmetric Noncommutative Torus

Ludwik Dąbrowski, Andrzej Sitarz
2015 Symmetry, Integrability and Geometry: Methods and Applications  
We introduce a family of spectral triples that describe the curved noncommutative two-torus. The relevant family of new Dirac operators is given by rescaling one of two terms in the flat Dirac operator. We compute the dressed scalar curvature and show that the Gauss-Bonnet theorem holds (which is not covered by the general result of Connes and Moscovici).
doi:10.3842/sigma.2015.075 fatcat:gqyxo5szovea7lbrtj57ughwsy