01079nas a2200133   4500008004100000245006300041210006300104260003200167520063100199100002000830700002200850700002200872856005100894       2014                        en  d00aDirac operators on noncommutative principal circle bundles0 aDirac operators on noncommutative principal circle bundles  bWorld Scientific Publishing3 aWe study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle. Examples of low-dimensional noncommutative tori are analyzed in more detail and all connections found that are compatible with an admissible Dirac operator. Conversely, a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection is exhibited. These examples are extended to the theta-deformed principal U(1)-bundle S 3 θ → S2.1 aSitarz, Andrzej1 aZucca, Alessandro1 aDabrowski, Ludwik  uhttp://urania.sissa.it/xmlui/handle/1963/35125