Einstein metrics on the ten-sphere

Jan Nienhaus; Matthias Wink

doi:10.4171/jems/1668

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Einstein metrics on the ten-sphere

Jan Nienhaus
University of California, Los Angeles, USA
ORCID
Matthias Wink
University of California, Santa Barbara, USA
ORCID

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Abstract

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

Cite this article

Jan Nienhaus, Matthias Wink, Einstein metrics on the ten-sphere. J. Eur. Math. Soc. (2025), published online first

DOI 10.4171/JEMS/1668