4-dimensional (para)-K\"ahler--Weyl structures

TL;DR

This paper proves the existence and uniqueness of para-Kaehler--Weyl structures on 4-dimensional para-Hermitian manifolds and extends the result to 4-dimensional pseudo-Hermitian manifolds via analytic continuation.

Contribution

It provides an elementary proof of the unique para-Kaehler--Weyl structure in 4D para-Hermitian manifolds and extends this to pseudo-Hermitian manifolds using analytic continuation.

Findings

Unique para-Kaehler--Weyl structures exist on 4D para-Hermitian manifolds.

Extension of the existence result to 4D pseudo-Hermitian manifolds.

Elementary proof technique for the structures.

Abstract

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.