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PreprintarXiv licencearXiv

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≥2 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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Cite

BibTeXRIS
BibTeX
@misc{hu2026transverse,
  title = {{Transverse rational curves and the LeBrun--Salamon conjecture}},
  author = {Zhengyu Hu and Kefeng Liu and Xueyuan Wan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10410},
  eprint = {2610.10410},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10410},
}
RIS
TY  - UNPB
TI  - Transverse rational curves and the LeBrun--Salamon conjecture
AU  - Zhengyu Hu
AU  - Kefeng Liu
AU  - Xueyuan Wan
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10410
UR  - https://arxiv.org/abs/2610.10410
AB  - We prove that every compact connected positive quaternionic--Kähler manifold of real dimension 4n with n≥2 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.
ER  -