New Non-naturally reductive Einstein metrics on Exceptional simple Lie groups

摘要

In this article, we achieved several non-naturally reductive Einstein metricson exceptional simple Lie groups, which are formed by the decomposition arisingfrom general Wallach spaces. By using the decomposition corresponding to thetwo involutive automorphisms, we calculated the non-zero coefficients in theexpression for the components of Ricci tensor with respect to the givenmetrics. The Einstein metrics are obtained as solutions of systems polynomialequations, which we manipulate by symbolic computations using Gr\"{o}bnerbases.