论文标题
Hermitian歧管带有平坦的高齿连接
Hermitian manifolds with flat Gauduchon connections
论文作者
论文摘要
我们完成了紧凑型隐性歧管的分类，该分类承认平坦的高杜琴连接。特别是，我们建立了杨和郑的猜想，表明除了平坦的Chern或Bismut连接的情况外，此类歧管是Kähler。更普遍地，我们证明，当扁平度假设被所谓的Kähler样条件取代时，我们证明了同样的结果，证明了Angella，Otal，Otal，Ugarte和Villacampa的猜想。我们还治疗了非紧凑型情况。
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 Kähler. More generally, we prove the same result holds when the flatness assumption is replaced by the so-called Kähler-like condition, proving a conjecture of Angella, Otal, Ugarte and Villacampa. We also treat the non-compact case.
