Complete Solution of Hadamard's Problem for the Scalar Wave Equation on   Petrov type III Space-Times
  We prove that there are no Petrov type III space-times on which the conformally invariant (self-adjoint) scalar wave equation or the non-self-adjoint scalar wave equation satisfies Huygens' principle. 
S. R. Czapor, R. G. McLenaghan and F. D. Sasse