Potential one-forms for hyperk\"ahler structures with torsion
  It is shown that an HKT-space with closed parallel potential 1-form has $D(2,1;-1)$-symmetry. Every locally conformally hyperk\"ahler manifold generates this type of geometry. The HKT-spaces with closed parallel potential 1-form arising in this way are characterized by their symmetries and an inhomogeneous cubic condition on their torsion. 
Liviu Ornea, Yat Sun Poon, Andrew Swann