T-duality revisited

We revisit the transformation rules of the metric and Kalb-Ramond field under T-duality, and express the corresponding relations in terms of the metric G and the field strength H = dB. In the course of the derivation, we find an explanation for potential reductions of the isometry group in the dual background. The formalism employed in this paper is illustrated with examples based on tori and spheres, where for the latter we construct a new non-geometric background.