Einstein metrics on the Ten-Sphere

TL;DR

This paper proves the existence of three new non-round Einstein metrics with positive scalar curvature on the 10-sphere, expanding the known examples beyond the previously known cases on S^6 and S^8.

Contribution

It demonstrates the existence of non-round Einstein metrics on S^{10}, a previously unknown case in even-dimensional spheres.

Findings

Three non-round Einstein metrics on S^{10} proven to exist.

First such metrics found on S^{10} beyond S^6 and S^8.

Advances understanding of Einstein metrics on spheres.

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 $S^8.$