4-dimensional (para)-Kähler-Weyl structures

Abstract

Abstract. We give an elementary proof of the fact that any 4-dimensional para-Hermitian manifold admits a unique para-Kähler-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 Kähler-Weyl structure.