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Annals of Global Analysis and Geometry

, Volume 37, Issue 2, pp 185–219 | Cite as

Invariant Einstein metrics on flag manifolds with four isotropy summands

  • Andreas Arvanitoyeorgos
  • Ioannis ChrysikosEmail author
Original Paper

Abstract

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.

Keywords

Homogeneous manifold Einstein metric Generalized flag manifold Isotropy representation \({\mathfrak{t}}\)-roots 

Mathematics Subject Classification (2000)

Primary 53C25 Secondary 53C30 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PatrasRionGreece

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