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Hitchin's α-invariant and positive sectional curvature on homotopy $9$-spheres

  • Yang-Hui He
  • Ziran Liu
  • Shing-Tung Yau
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Abstract

We prove that a smooth homotopy $9$-sphere admits a Riemannian metric of positive sectional curvature if and only if its Hitchin α-invariant vanishes, or equivalently if and only if it admits a Riemannian metric of positive scalar curvature.

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Cite

BibTeXRIS
BibTeX
@misc{he2026hitchins,
  title = {{Hitchin's $α$-invariant and positive sectional curvature on homotopy $9$-spheres}},
  author = {Yang-Hui He and Ziran Liu and Shing-Tung Yau},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33474},
  eprint = {2610.33474},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33474},
}
RIS
TY  - UNPB
TI  - Hitchin's α-invariant and positive sectional curvature on homotopy $9$-spheres
AU  - Yang-Hui He
AU  - Ziran Liu
AU  - Shing-Tung Yau
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33474
UR  - https://arxiv.org/abs/2610.33474
AB  - We prove that a smooth homotopy $9$-sphere admits a Riemannian metric of positive sectional curvature if and only if its Hitchin α-invariant vanishes, or equivalently if and only if it admits a Riemannian metric of positive scalar curvature.
ER  -