Almost complex structures that are harmonic maps

TL;DR

This paper explores geometric conditions under which the almost complex structure of a four-dimensional almost Hermitian manifold acts as a harmonic map or minimal isometric embedding into its twistor space.

Contribution

It establishes new geometric criteria for harmonicity and minimality of almost complex structures in four-dimensional almost Hermitian manifolds.

Findings

Conditions for harmonicity of the almost complex structure.

Criteria for minimal isometric embedding into twistor space.

Insights into the geometry of four-dimensional almost Hermitian manifolds.

Abstract

We find geometric conditions on a four-dimensional almost Hermitian manifold under which the almost complex structure is a harmonic map or a minimal isometric imbedding of the manifold into its twistor space.