Asian Journal of Mathematics
Volume 26 (2022)
On the stability of homogeneous Einstein manifolds
Pages: 555 – 584
Let $g$ be a $G$-invariant Einstein metric on a compact homogeneous space $M = G/K$. We use a formula for the Lichnerowicz Laplacian of $g$ at $G$-invariant $TT$-tensors to study the stability type of $g$ as a critical point of the scalar curvature function. The case when $g$ is naturally reductive is studied in special detail.
Einstein, homogeneous, stability
2010 Mathematics Subject Classification
This research was partially supported by a grant from the Universidad Nacional de Córdoba, Argentina.
Received 27 May 2022
Accepted 17 June 2022
Published 24 March 2023