Geometriae Dedicata

, Volume 160, Issue 1, pp 261–285 | Cite as

Einstein metrics on compact Lie groups which are not naturally reductive

  • Andreas ArvanitoyeorgosEmail author
  • Kunihiko Mori
  • Yusuke Sakane
Original Paper


The study of left-invariant Einstein metrics on compact Lie groups which are naturally reductive was initiated by D’Atri and Ziller (Mem Am Math Soc 18, (215) 1979). In 1996 the second author obtained non-naturally reductive Einstein metrics on the Lie group SU(n) for n ≥  6, by using a method of Riemannian submersions. In the present work we prove existence of non-naturally reductive Einstein metrics on the compact simple Lie groups SO(n) (n ≥  11), Sp(n) (n ≥  3), E 6, E 7, and E 8.


Einstein metrics Homogeneous spaces Naturally reductive metrics Kähler C-spaces 

Mathematics Subject Classification (2000)

53C25 53C30 17B20 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Andreas Arvanitoyeorgos
    • 1
    Email author
  • Kunihiko Mori
    • 2
  • Yusuke Sakane
    • 3
  1. 1.Department of MathematicsUniversity of PatrasRionGreece
  2. 2.Saibi-Heisei Junior & Senior High SchoolMatsuyama, EhimeJapan
  3. 3.Department of Pure and Applied Mathematics, Graduate School of Information Science and TechnologyOsaka UniversityToyonaka, OsakaJapan

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