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arXiv · 2108.08181

On Gauduchon K\"ahler-like manifolds

Quanting Zhao·Fangyang Zheng
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Abstract

In a paper by Angella, Otal, Ugarte, and Villacampa, the authors conjectured that on a compact Hermitian manifold, if a Gauduchon connection other than Chern or Strominger is K\"ahler-like, then the Hermitian metric must be K\"ahler. They also conjectured that if two Gauduchon connections are both K\"ahler-like, then the metric must be K\"ahler. In this paper, we discuss some partial answers to the first conjecture, and give a proof to the second conjecture. In the process, we discovered an interesting `duality' phenomenon amongst Gauduchon connections, which seems to be intimately tied to the question, though we do not know if there is any underlying reason for that from physics.

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Quanting Zhao, Fangyang Zheng. 2021-08-18. On Gauduchon K\"ahler-like manifolds. https://arxiv.org/abs/2108.08181

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