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

2025/02/17 by Arvanitoyeorgos, Andreas, Sakane, Yusuke, Statha, Marina
#13P10 #53C25 #53C30 #65H10 #68W30 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.18491

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(k₁+⋯ +k_p)/\s(\U(k₁)×⋯×\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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