On generalized Gauduchon metrics

TL;DR

This paper investigates a broad class of Hermitian metrics called generalized Gauduchon metrics, exploring their properties, examples, and generalizations on various complex manifolds.

Contribution

It introduces and studies a new class of Hermitian metrics that generalize Gauduchon metrics, including explicit examples on diverse manifolds.

Findings

Examples on nilmanifolds and Sasakian products

Metrics with $ ext{d} ext{d}^c$-closed fundamental forms

Construction via twist methods

Abstract

We study a class of Hermitian metrics on complex manifolds, recently introduced by J. Fu, Z. Wang and D. Wu, which are a generalization of Gauduchon metrics. This class includes the one of Hermitian metrics for which the associated fundamental 2-form is $\partial \bar\partial$-closed. Examples are given on nilmanifolds, on products of Sasakian manifolds, on $S^1$-bundles and via the twist construction introduced by A. Swann.