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2 results

  • Homogeneous Einstein Manifolds with Vanishing $S$ Curvature

  • Part of
  • Libing Huang, Zhongmin Shen
  • Journal:
    Canadian Mathematical Bulletin / Volume 62 / Issue 3 / September 2019
    Published online by Cambridge University Press:
    22 February 2019, pp. 525-537
    Print publication:
    September 2019
    • Article
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  • Infinitely many new Einstein Finsler metrics are constructed on several homogeneous spaces. By imposing certain conditions on the homogeneous spaces, it is shown that the Ricci constant condition becomes an ordinary differential equation. The regular solutions of this equation lead to a two parameter family of Einstein Finsler metrics with vanishing $S$ curvature.

  • INVARIANT EINSTEIN METRICS ON GENERALIZED FLAG MANIFOLDS WITH TWO ISOTROPY SUMMANDS

  • Part of
  • ANDREAS ARVANITOYEORGOS, IOANNIS CHRYSIKOS
  • Journal:
    Journal of the Australian Mathematical Society / Volume 90 / Issue 2 / April 2011
    Published online by Cambridge University Press:
    19 July 2011, pp. 237-251
    Print publication:
    April 2011
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  • Let M=G/K be a generalized flag manifold, that is, an adjoint orbit of a compact, connected and semisimple Lie group G. We use a variational approach to find non-Kähler homogeneous Einstein metrics for flag manifolds with two isotropy summands. We also determine the nature of these Einstein metrics as critical points of the scalar curvature functional under fixed volume.