Pseudo-harmonic Hermitian structures on Weyl manifolds

TL;DR

This paper investigates geometric conditions on Hermitian-Weyl manifolds that make the complex structure a pseudo-harmonic map into the twistor space, focusing on four-dimensional or locally conformally Kähler cases.

Contribution

It establishes new geometric criteria for Hermitian-Weyl structures to have their complex structure as a pseudo-harmonic map, extending previous understanding in specific manifold classes.

Findings

Identifies conditions under which the complex structure is pseudo-harmonic

Focuses on four-dimensional and locally conformally Kähler Hermitian-Weyl manifolds

Provides a link between Hermitian-Weyl geometry and twistor space mappings

Abstract

We find geometric conditions on a Hermitian-Weyl manifold under which the complex structure is a pseudo-harmonic map in the sense of G. Kokarev \cite{K09} from the manifold into its twistor space. This is done under the assumption that the dimension of the manifold is four or the Hermitian-Weyl structure is locally conformally K\"ahler.