4-dimensional (para)-K\"ahler--Weyl structures
  We give an elementary proof of the fact that any 4-dimensional para-Hermitian manifold admits a unique para-Kaehler--Weyl structure. We then use analytic continuation to pass from the para-complex to the complex setting and thereby show any 4-dimensional pseudo-Hermitian manifold also admits a unique Kaehler--Weyl structure. 
Peter Gilkey and Stana Nikcevic
math.DG