On the stability of homogeneous Einstein manifolds

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.

Keywords

Einstein, homogeneous, stability

2010 Mathematics Subject Classification

53C25

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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