Nearly $G_2$-manifolds and $G_2$-Laplacian co-flows
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908859473330176 |
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| author | Lotay, Jason D. Stein, Jakob |
| author_facet | Lotay, Jason D. Stein, Jakob |
| contents | Nearly $G_2$-structures define positive Einstein metrics in $7$ dimensions and are critical points, up to scale, for a geometric flow of co-closed $G_2$-structures with good analytic properties called the modified $G_2$-Laplacian co-flow. We introduce a suitable normalization of this flow so that nearly $G_2$-structures are stable under rescaling. However, we show that many nearly $G_2$-structures are unstable for this flow: specifically, all those naturally arising from 3-Sasakian geometry. In particular, we demonstrate that the standard nearly $G_2$-structure on the round 7-sphere is an unstable critical point with high index. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nearly $G_2$-manifolds and $G_2$-Laplacian co-flows Lotay, Jason D. Stein, Jakob Differential Geometry 53C44, 53C25, 53C10 Nearly $G_2$-structures define positive Einstein metrics in $7$ dimensions and are critical points, up to scale, for a geometric flow of co-closed $G_2$-structures with good analytic properties called the modified $G_2$-Laplacian co-flow. We introduce a suitable normalization of this flow so that nearly $G_2$-structures are stable under rescaling. However, we show that many nearly $G_2$-structures are unstable for this flow: specifically, all those naturally arising from 3-Sasakian geometry. In particular, we demonstrate that the standard nearly $G_2$-structure on the round 7-sphere is an unstable critical point with high index. |
| title | Nearly $G_2$-manifolds and $G_2$-Laplacian co-flows |
| topic | Differential Geometry 53C44, 53C25, 53C10 |
| url | https://arxiv.org/abs/2505.14121 |