Quaternionic Torsion Geometry, Superconformal Symmetry and T‐duality

HyperKähler metrics with torsion (HKT metrics) are constructed via superconformal symmetry. It is shown how T‐duality interpreted as a twist construction for circle actions provides a number of compact simply‐connected examples. Further applications of the twist construction are discussed to obtain compact simply‐connected HKT manifolds with few symmetries and to construct all HKT nilmanifolds.