Conformal flatness, non-Abelian Kaluza-Klein and the Quaternions
  Maximally symmetric manifolds with holonomy in the unitary quaternionic group Sp(d/4) emerge from the non-Abelian Kaluza-Klein reduction of conformally flat spaces. Thus, all special manifolds with constant properly `holonomy-related' sectional curvature, are in natural correspondence with conformally flat, possibly non-Abelian, Kaluza-Klein spaces. 
Paolo Maraner, Jiannis K. Pachos
math-ph hep-th math.MP quant-ph