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Einstein metrics on the Ten-Sphere

Differential Geometry 2024-09-12 v3

Abstract

We prove the existence of three non-round, non-isometric Einstein metrics with positive scalar curvature on the sphere S10.S^{10}. Previously, the only even-dimensional spheres known to admit non-round Einstein metrics were S6S^6 and S8.S^8.

Keywords

Cite

@article{arxiv.2303.04832,
  title  = {Einstein metrics on the Ten-Sphere},
  author = {Jan Nienhaus and Matthias Wink},
  journal= {arXiv preprint arXiv:2303.04832},
  year   = {2024}
}

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references updated

R2 v1 2026-06-28T09:08:06.423Z