The qc Yamabe problem on non-spherical quaternionic contact manifolds
  It is shown that the qc Yamabe problem has a solution on any compact qc manifold which is non-locally qc equivalent to the standard 3-Sasakian sphere. Namely, it is proved that on a compact non-locally spherical qc manifold there exists a qc conformal qc structure with constant qc scalar curvature 
Stefan Ivanov and Alexander Petkov
math.DG