Stability of non-diagonal Einstein metrics on homogeneous spaces $H\times H/ ΔK$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910606779482112 |
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| author | Gutiérrez, Valeria |
| author_facet | Gutiérrez, Valeria |
| contents | We consider the homogeneous space $M=H\times H/ΔK$, where $H/K$ is an irreducible symmetric space and $ΔK$ denotes diagonal embedding. Recently, Lauret and Will provided a complete classification of $H\times H$-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 $H\times H$-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 $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10686 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of non-diagonal Einstein metrics on homogeneous spaces $H\times H/ ΔK$ Gutiérrez, Valeria Differential Geometry We consider the homogeneous space $M=H\times H/ΔK$, where $H/K$ is an irreducible symmetric space and $ΔK$ denotes diagonal embedding. Recently, Lauret and Will provided a complete classification of $H\times H$-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 $H\times H$-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 $M$. |
| title | Stability of non-diagonal Einstein metrics on homogeneous spaces $H\times H/ ΔK$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2409.10686 |