Biconformal changes of metric and pseudo-harmonic morphisms
  Pseudo-harmonic morphisms give rise on the domain space to a distribution which admits an almost complex structure compatible with the given Riemannian metric. We shall show that this property, together with the harmonicity, are preserved by a biconformal change of the domain metric. The special case of the pseudo-horizontally homothetic harmonic morphisms is also treated. 
Radu Slobodeanu