New Einstein metrics on the Lie group \(\mathrm{SO}(n)\) which are not naturally reductive (Q315577)

This paper presents a well-organized and detailed study of left-invariant Einstein metrics on the compact Lie group \(\mathrm{SO}(n)\). The authors impose certain symmetry assumptions in the set of all left-invariant metrics on \(\mathrm{SO}(n)\) and compute the Ricci tensor for those metrics. They apply an interesting approach to obtain new Einstein metrics which are not naturally reductive -- as solutions of systems of polynomial equations manipulated by symbolic computations using Gröbner bases.