Holomorphic submersions onto K\"ahler or balanced manifolds

TL;DR

This paper investigates the properties of compact complex manifolds with holomorphic submersions onto K"ahler or balanced manifolds, extending several classical results in complex geometry.

Contribution

It generalizes existing results on weak K"ahlerianity for manifolds admitting holomorphic submersions onto K"ahler or balanced targets.

Findings

Extended Harvey and Lawson's results to new contexts

Generalized Michelson's balanced manifold results

Provided new insights into weak K"ahlerianity properties

Abstract

We study many properties concerning weak K\"ahlerianity on compact complex manifolds which admits a holomorphic submersion onto a K\"ahler or a balanced manifold. We get generalizations of some results of Harvey and Lawson (the K\"ahler case), Michelson (the balanced case), Popovici (the sG case) and others.