Harmonic morphisms between almost Hermitian manifolds

TL;DR

This paper investigates conditions on Lee forms that determine when holomorphic maps between almost Hermitian manifolds are harmonic or morphisms, and explores properties of holomorphic maps related to cosymplectic and Hermitian structures.

Contribution

It provides new criteria involving Lee forms for harmonicity and morphisms of holomorphic maps between almost Hermitian manifolds, and examines their geometric implications.

Findings

Conditions on Lee form for harmonic maps established

Criteria for holomorphic maps to preserve cosymplectic structures

Conditions under which holomorphic maps induce Hermitian structures

Abstract

We obtain conditions on the Lee form under which a holomorphic map between almost Hermitian manifolds is a harmonic map or morphism. Then we discuss under what conditions (i) the image of a holomorphic map from a cosymplectic manifold is also cosymplectic, (ii) a holomophic map with Hermitian image defines a Hermitian structure on its domain.