Homogeneous Einstein metrics and local maxima of the Hilbert action

TL;DR

This paper investigates specific homogeneous Einstein metrics and demonstrates that three infinite families cannot serve as local maxima of the Hilbert action, refining the understanding of stability in geometric analysis.

Contribution

It rules out three infinite families of neutrally stable homogeneous Einstein metrics as local maxima of the Hilbert action.

Findings

Three infinite families of neutrally stable homogeneous Einstein metrics are ruled out as local maxima.

The results refine the stability landscape of Einstein metrics in geometric analysis.

Abstract

In this short note, three infinite families of neutrally stable homogeneous Einstein metrics are ruled out as candidates for local maxima of the Hilbert action.