Holomorphic harmonic morphisms from cosymplectic almost Hermitian manifolds

TL;DR

This paper investigates conditions under which certain geometric structures on 4-dimensional Riemannian manifolds, specifically cosymplectic almost Hermitian structures, relate to minimal conformal foliations and integrability of distributions.

Contribution

It establishes a characterization linking cosymplectic structures to Riemannian foliations and integrability of the horizontal distribution in 4D manifolds.

Findings

Both adapted almost Hermitian structures are cosymplectic iff the foliation is Riemannian and horizontal distribution is integrable.

Provides a geometric criterion for cosymplecticity in terms of foliation properties.

Enhances understanding of harmonic morphisms in the context of cosymplectic geometry.

Abstract

We study 4-dimensional Riemannian manifolds equipped with a minimal and conformal foliation $\mathcal F$ of codimension 2. We prove that the two adapted almost Hermitian structures $J_1$ and $J_2$ are both cosymplectic if and only if $\mathcal F$ is Riemannian and its horizontal distribution $\mathcal H$ is integrable.