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Non naturally reductive Einstein metrics on the orthogonal group via real flag manifolds
Published 17 Sep 2024 in math.DG | (2409.18990v1)
Abstract: 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 $\SO(k_1+\cdots +k_p)/\SO(k_1)\times\cdots\times\SO(k_p)$ and by imposing certain symmetry assumptions in the set of all left-invariant metrics on $\SO(n)$.
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