Homogeneous Einstein metrics on 𝐺₂/𝑇

Arvanitoyeorgos, Andreas; Chrysikos, Ioannis; Sakane, Yusuke

doi:10.1090/S0002-9939-2013-11682-5

Homogeneous Einstein metrics on $G_2/T$
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by Andreas Arvanitoyeorgos, Ioannis Chrysikos and Yusuke Sakane PDF

Proc. Amer. Math. Soc. 141 (2013), 2485-2499 Request permission

Abstract:

We construct the Einstein equation for an invariant Riemannian metric on the exceptional full flag manifold $M=G_2/T$. By computing a Gröbner basis for a system of polynomials on six variables we prove that this manifold admits exactly two non-Kähler invariant Einstein metrics. Thus $G_2/T$ turns out to be the first known example of an exceptional full flag manifold which admits a non-Kähler and not normal homogeneous Einstein metric.

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