Stability of non-diagonal Einstein metrics on homogeneous spaces H× H/ ΔK

2024/09/16 by Valeria Gutiérrez, Gutiérrez, Valeria
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2409.10686

openalex publication_date 2024/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the homogeneous space M=H× H/ΔK, where H/K is an irreducible symmetric space and ΔK denotes diagonal embedding. Recently, Lauret and Will provided a complete classification of H× H-invariant Einstein metrics on M. They obtained that there is always at least one non-diagonal Einstein metric on M, and in some cases, diagonal Einstein metrics also exist. We give a formula for the scalar curvature of a subset of H× H-invariant metrics and study the stability of non-diagonal Einstein metrics on M with respect to the Hilbert action, obtaining that these metrics are unstable with different coindexes for all homogeneous spaces M.

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