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arXiv · 2610.10410

Transverse rational curves and the LeBrun--Salamon conjecture

Zhengyu Hu·Kefeng Liu·Xueyuan Wan
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Abstract

We prove that every compact connected positive quaternionic--Kähler manifold of real dimension $4n$ with $n\ge2$ is isometric to a Wolf space after rescaling the metric by a positive constant. This proves the LeBrun--Salamon conjecture. The proof uses transverse rational curves and the contact structure of the twistor space.

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Zhengyu Hu, Kefeng Liu, Xueyuan Wan. 2026-10-07. Transverse rational curves and the LeBrun--Salamon conjecture. https://arxiv.org/abs/2610.10410

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