A Note on Fluxes in Six-Dimensional String Theory Backgrounds
  We study the structure of warped compactifications of type IIB string theory to six space-time dimensions. We find that the most general four-manifold describing the internal dimensions is conformal to a Kahler manifold, in contrast with the heterotic case where the four-manifold must be conformally Calabi-Yau. 
Katrin Becker and Li-Sheng Tseng