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arXiv · 2502.18491

Non naturally reductive Einstein metrics on $\SU(N)$ via generalized flag manifolds

Andreas Arvanitoyeorgos·Yusuke Sakane·Marina Statha
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Abstract

We obtain new invariant Einstein metrics on the compact Lie group $\SU(N)$ which are not naturally reductive. This is achieved by using the generalized flag manifold $G/K=\SU(k_1+\cdots +k_p)/\s(\U(k_1)\times\cdots\times\U(k_p))$ and by taking an appropriate choice of orthogonal basis of the center of Lie subalgebra $\frak k$ for $K$, which poses certain symmetry conditions to the $\Ad(K)$-invariant metrics of $\SU(N)$. We also study the isometry problem for the Einstein metrics found.

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Andreas Arvanitoyeorgos, Yusuke Sakane, Marina Statha. 2025-02-17. Non naturally reductive Einstein metrics on $\SU(N)$ via generalized flag manifolds. https://doi.org/10.1016/j.geomphys.2025.105575

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