Invariant Einstein metrics on flag manifolds with four isotropy summands

By Andreas Arvanitoyeorgos, Ioannis Chrysikos. 2009

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A generalized flag manifold is a homogeneous space of the form G/K, where K is the centralizer of a torus in a compact connected semisimple Lie group G. We classify all flag manifolds with four isotropy summands by the use of $${\mathfrak{t}}$$-roots. We present new G-invariant Einstein metrics by solving explicity the Einstein equation. We also examine the isometric problem for these Einstein metrics.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/92d337a81563a23fcf3a6c3b7be0985980c48089