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arXiv · 2107.00354

On the stability of homogeneous Einstein manifolds II

Jorge Lauret·Cynthia E. Will
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Abstract

For any $G$-invariant metric on a compact homogeneous space $M=G/K$, we give a formula for the Lichnerowicz Laplacian restricted to the space of all $G$-invariant symmetric $2$-tensors in terms of the structural constants of $G/K$. As an application, we compute the $G$-invariant spectrum of the Lichnerowicz Laplacian for all the Einstein metrics on most generalized Wallach spaces and any flag manifold with $b_2(M)=1$. This allows to deduce the $G$-stability and critical point types of each of such Einstein metrics as a critical point of the scalar curvature functional.

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Jorge Lauret, Cynthia E. Will. 2021-07-01. On the stability of homogeneous Einstein manifolds II. https://arxiv.org/abs/2107.00354

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