The canonical Einstein metric on $G_{2}$ is dynamically unstable under the Ricci flow
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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2018
- DOI:
- 10.48550/arXiv.1808.00344
- arXiv:
- arXiv:1808.00344
- Bibcode:
- 2018arXiv180800344H
- Keywords:
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- Mathematics - Differential Geometry
- E-Print:
- 7 pages