Stability of nearly Kähler and nearly parallel $G_2$-manifolds
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912107984846848 |
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| author | Solé-Farré, Enric |
| author_facet | Solé-Farré, Enric |
| contents | We investigate generalisations of Hitchin's functionals, whose critical points correspond to nearly Kähler and nearly parallel $G_2$-structures. Our focus is on the gradient flow of these functionals and the spectral decomposition of their Hessians with respect to natural indefinite inner products.
We introduce a Morse-like index for these functionals, termed the Hitchin index. We prove this index provides a lower bound for the Einstein co-index and explore its relationship with the deformation theory of $G_2$- and $\operatorname{Spin}(7)$-conifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21103 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of nearly Kähler and nearly parallel $G_2$-manifolds Solé-Farré, Enric Differential Geometry 53C10, 53C25, 53C29, 53C55 We investigate generalisations of Hitchin's functionals, whose critical points correspond to nearly Kähler and nearly parallel $G_2$-structures. Our focus is on the gradient flow of these functionals and the spectral decomposition of their Hessians with respect to natural indefinite inner products. We introduce a Morse-like index for these functionals, termed the Hitchin index. We prove this index provides a lower bound for the Einstein co-index and explore its relationship with the deformation theory of $G_2$- and $\operatorname{Spin}(7)$-conifolds. |
| title | Stability of nearly Kähler and nearly parallel $G_2$-manifolds |
| topic | Differential Geometry 53C10, 53C25, 53C29, 53C55 |
| url | https://arxiv.org/abs/2410.21103 |