Stability of the Non-Symmetric Space $E_7/\mathrm{PSO}(8)$

TL;DR

This paper demonstrates that the normal metric on the homogeneous space E_7/PSO(8) is stable under the Einstein-Hilbert action, providing the first example of a non-symmetric positive scalar curvature metric with this stability.

Contribution

It presents the first known example of a non-symmetric metric of positive scalar curvature that is stable under the Einstein-Hilbert action.

Findings

Normal metric on E_7/PSO(8) is stable

First example of non-symmetric stable positive scalar curvature metric

Stability under Einstein-Hilbert action confirmed

Abstract

We prove that the normal metric on the homogeneous space $E_7/\mathrm{PSO}(8)$ is stable with respect to the Einstein-Hilbert action, thereby exhibiting the first known example of a non-symmetric metric of positive scalar curvature with this property.