TWISTOR SPACES FOR QKT MANIFOLDS

We find that the target space of two-dimensional (4,0) supersymmetric sigma models with torsion coupled to (4,0) supergravity is a QKT manif old, that is, a quaternionic Kahler manifold with torsion. We give fou r examples of geodesically complete QKT manifolds, one of which is a g eneralisation of the LeBrun geometry. We then construct the twister sp ace associated with a QKT manifold and show that under certain conditi ons it is a Kahler manifold with a complex contact structure. We also show that, for same 4k-dimensional QKT manifold, there is an associate d 4(k+1)-dimensional hyper-Kahler one.