Invariant Einstein metrics on real flag manifolds with two or three isotropy summands

2019/07/05 by Brian Grajales, Lino Grama, Grajales, Brian +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1907.02626

This (second) version is substantially expanded with respect to the first version. New title

arxiv created 2020/07/02 · arxiv updated 2020/07/06

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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