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New Einstein metrics on the Lie group $SO(n)$ which are not naturally reductive (1511.08849v1)
Published 25 Nov 2015 in math.DG
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 Gr\"obner bases.