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

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.

v1: 23 pages. v2: 21 pages, 3 tables. Restructured and streamlined. v3: Revised version. 22 pages, 3 tables