Quaternionic contact manifolds with a closed fundamental 4-form
  We show that the fundamental 4-form on a quaternionic contact manifold of dimension at least eleven is closed if and only if the torsion endomorphism of the Biquard connection vanishes. This condition characterizes quaternionic contact structures which are locally qc homothetic to 3-Sasakian structures. 
Stefan Ivanov and Dimiter Vassilev