Harmonic Hermitian structures on Riemannian manifolds with skew-torsion

TL;DR

This paper investigates conditions under which a complex structure on a four-dimensional Hermitian manifold with skew-torsion acts as a harmonic map into its twistor space, linking geometric structures with harmonic map theory.

Contribution

It establishes new geometric conditions for harmonicity of complex structures on Hermitian manifolds with skew-torsion, expanding understanding of harmonic maps in complex geometry.

Findings

Derived conditions for harmonic complex structures with skew-torsion

Connected Hermitian geometry with twistor space harmonic maps

Enhanced understanding of metric connections with skew-torsion

Abstract

We find geometric conditions on a four-dimensional Hermitian manifold endowed with a metric connection with totally skew-symmetric torsion under which the complex structure is a harmonic map from the manifold into its twistor space considered with a natural family of Riemannian metrics defined by means of the metric and the given connection on the base manifold.