具有平坦 Gauduchon 联络的 Hermite 流形
微分几何
2022-07-20 v2
摘要
我们完成了对容许平坦 Gauduchon 联络的紧致 Hermite 流形的分类。特别地，我们确立了 Yang 和 Zheng 的一个猜想，表明除平坦 Chern 或 Bismut 联络的情形外，此类流形为 K"ahler 流形。更一般地，我们证明当平坦性假设被所谓的类 K"ahler 条件替代时同样结论成立，从而证明了 Angella、Otal、Ugarte 和 Villacampa 的一个猜想。我们也处理了非紧情形。
引用
@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}
}
备注
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