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arXiv · 2204.08170

Hermitian manifolds with flat Gauduchon connections

Ramiro A. Lafuente·James Stanfield
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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.

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Ramiro A. Lafuente, James Stanfield. 2022-04-18. Hermitian manifolds with flat Gauduchon connections. https://arxiv.org/abs/2204.08170

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