Non Naturally Reductive Einstein Metrics on the Orthogonal Group via Real Flag Manifolds.

We obtain new invariant Einstein metrics on the compact Lie groups SO (n) which are not naturally reductive. This is achieved by using the real flag manifolds SO (k 1 + ⋯ + k p) / SO (k 1) × ⋯ × SO (k p) and by imposing certain symmetry assumptions in the set of all left-invariant metrics on SO (n) . [ABSTRACT FROM AUTHOR]