Mirror symmetry relates two Calabi-Yau threefolds with mirrored Hodge diamonds. Since Calabi-Yau threefold is Kahler, this naive correspondence does not hold for rigid Calabi-Yau threefolds. Here Calabi-Yau theefold is called rigid if it has no complex deformation, i.e. $h^{2,1}=0$.

I heard that a "mirror manifold" of a rigid Calabi-Yau threefold is singularity theory, or Landau-Ginzburg theory. Are there any good explanation for this? Or can someone suggest a good reference for this (I am a math grad student with little physics background)?