2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/202799We classify non-dilatonic NS-NS type II supergravity backgrounds admitting a consistent absolute parallelism. They are all given by parallelised Lie groups admitting scalar flat bi-invariant lorentzian metrics. There are seven different classes, some of them containing moduli. For each class we determine the amount of supersymmetry which is preserved: there are examples with 16, 18, 20, 22, 24, 28 and 32 supersymmetries.14 pages (v2: corrected comments about the dilaton; v3: corrected the list of solutions after properly taking into account the dilaton equation; v4: added one reference)High Energy Physics - TheoryDifferential Geometrytext