On the stability of homogeneous Einstein manifolds

DOI10.4310/AJM.2022.V26.N4.A3arXiv2105.06336MaRDI QIDQ6367589

Publication date: 13 May 2021

Abstract: 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.

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25) Global Riemannian geometry, including pinching (53C20)

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