Homogeneous Einstein metrics on G₂/T

الأصل · EN

We construct the Einstein equation for an invariant Riemannian metric on the exceptional full flag manifold M=G₂/T. By computing a Gröbner basis for a system of polynomials of multi-variables we prove that this manifold admits exactly two non-Kähler invariant Einstein metrics. Thus G₂/T turns out to be the first known example of an exceptional full flag manifold which admits at least one non-Kähler and not normal homogeneous Einstein metric.