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Invariant Einstein metrics on real flag manifolds with two or three isotropy summands (1907.02626v2)
Published 5 Jul 2019 in math.DG
Abstract: We study the existence of invariant Einstein metrics on real flag manifolds associated to simple and non-compact split real forms of complex classical Lie algebras whose isotropy representation decomposes into two or three irreducible sub-representations. In this situation, one can have equivalent sub-modules, leading to the existence of non-diagonal homogeneous Riemannian metrics. In particular, we prove the existence of non-diagonal Einstein metrics on real flag manifolds.
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