“…Notice that, in the particular case of a tensor hierarchy where all the fields do not depend on the internal space , the curvature reduces to the familiar equations of a doubled torus bundle, i.e. which is exactly the curvature of the ‐bundle araising in the case of a globally geometric T‐duality, as explained in [1]. Also the gauge transformations reduce to The local field can thus be globalized to the curvature of a doubled torus bundle with 1st Chern class .…”