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arXiv · 1511.08849

New Einstein metrics on the Lie group $SO(n)$ which are not naturally reductive

Andreas Arvanitoyeorgos·Yusuke Sakane·Marina Statha
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Abstract

We obtain new invariant Einstein metrics on the compact Lie groups $SO(n)$ ($n \geq 7$) which are not naturally reductive. This is achieved by imposing certain symmetry assumptions in the set of all left-invariant metrics on $SO(n)$ and by computing the Ricci tensor for such metrics. The Einstein metrics are obtained as solutions of systems polynomial equations, which we manipulate by symbolic computations using Gröbner bases.

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Andreas Arvanitoyeorgos, Yusuke Sakane, Marina Statha. 2015-11-25. New Einstein metrics on the Lie group $SO(n)$ which are not naturally reductive. https://arxiv.org/abs/1511.08849

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