The stability of standard homogeneous Einstein manifolds

Abstract

Back in 1985, Wang and Ziller obtained a complete classification of all homogeneous spaces of compact simple Lie groups on which the standard or Killing metric is Einstein. The list consists, beyond isotropy irreducible spaces, of 12 infinite families (two of them are actually conceptual constructions) and 22 isolated examples. We study in this paper the nature of each of these Einstein metrics as a critical point of the scalar curvature functional.

arXiv comment34 pages, 10 tables, 2 figures. Final version accepted in Math. Z

References in corpus (3)

• Stability and instability of Ricci solitons
• The stability of standard homogeneous Einstein manifolds
• Homogeneous Einstein metrics and local maxima of the Hilbert action

Cited by in corpus (5)

• The stability of standard homogeneous Einstein manifolds
• Compact geodesic orbit spaces with a simple isotropy group
• Homogeneous Einstein metrics and local maxima of the Hilbert action
• Linear stability of Perelman's $\nu$-entropy of standard Einstein manifolds
• Generalized Ricci flow on aligned homogeneous spaces