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arXiv · 1808.00344

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

Stuart James Hall
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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.

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Stuart James Hall. 2018-08-01. The canonical Einstein metric on $G_{2}$ is dynamically unstable under the Ricci flow. https://doi.org/10.1112/blms.12238

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