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arXiv · 2409.18990

Non naturally reductive Einstein metrics on the orthogonal group via real flag manifolds

Andreas Arvanitoyeorgos·Yusuke Sakane·Marina Statha
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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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Andreas Arvanitoyeorgos, Yusuke Sakane, Marina Statha. 2024-09-17. Non naturally reductive Einstein metrics on the orthogonal group via real flag manifolds. https://doi.org/10.1007/s00025-023-02068-1

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