The canonical Einstein metric on $G_{2}$ is dynamically unstable under the Ricci flow

Stuart James Hall

doi:10.1112/blms.12238

paper

The canonical Einstein metric on $G_{2}$ is dynamically unstable under the Ricci flow

arXiv:1808.00344 · doi:10.1112/blms.12238

Abstract

In this note we show that the bi-invariant Einstein metric on the compact Lie group $G_{2}$ is dynamically unstable as a fixed point of the Ricci flow. This completes the stability analysis for the bi-invariant metrics on the compact, connected, simple Lie groups. Interestingly, $G_{2}$ is the only unstable exceptional group.

7 pages; v2 typos fixed, rewritten following referee's suggestions, to appear in BLMS

The canonical Einstein metric on G2​ is dynamically unstable under the Ricci flow

Abstract

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The canonical Einstein metric on $G_{2}$ is dynamically unstable under the Ricci flow