Hermitian manifolds with flat Gauduchon connections
Abstract
We complete the classification of compact Hermitian manifolds admitting a flat Gauduchon connection. In particular, we establish a conjecture of Yang and Zheng, showing that apart from the cases of a flat Chern or Bismut connection, such manifolds are K\"ahler. More generally, we prove the same result holds when the flatness assumption is replaced by the so-called K\"ahler-like condition, proving a conjecture of Angella, Otal, Ugarte and Villacampa. We also treat the non-compact case.
Keywords
Cite
@article{arxiv.2204.08170,
title = {Hermitian manifolds with flat Gauduchon connections},
author = {Ramiro A. Lafuente and James Stanfield},
journal= {arXiv preprint arXiv:2204.08170},
year = {2022}
}
Comments
11 pages. Significant changes (including title) as the main theorem (Theorem 3.1) has been improved: The compactness assumption can be dropped with two possible exceptions and the flatness assumption has been relaxed to the Kaehler-like condition in all cases. Proof simplified and notation updated