On $G_2$ manifolds with cohomogeneity two symmetry
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914818125987840 |
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| author | Aslan, Benjamin Trinca, Federico |
| author_facet | Aslan, Benjamin Trinca, Federico |
| contents | We consider $G_2$ manifolds with a cohomogeneity two $\mathbb{T}^2\times \mathrm{SU}(2)$ symmetry group. We give a local characterization of these manifolds and we describe the geometry, including regularity and singularity analysis, of cohomogeneity one calibrated submanifolds in them. We apply these results to the manifolds recently constructed by Foscolo--Haskins--Nordström and to the Bryant--Salamon manifold of topology $S^3\times \mathbb{R}^4$. In particular, we describe new large families of complete $\mathbb{T}^2$-invariant associative submanifolds in them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_03569 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On $G_2$ manifolds with cohomogeneity two symmetry Aslan, Benjamin Trinca, Federico Differential Geometry 53C25, 53C29, 53C38, 53C40 We consider $G_2$ manifolds with a cohomogeneity two $\mathbb{T}^2\times \mathrm{SU}(2)$ symmetry group. We give a local characterization of these manifolds and we describe the geometry, including regularity and singularity analysis, of cohomogeneity one calibrated submanifolds in them. We apply these results to the manifolds recently constructed by Foscolo--Haskins--Nordström and to the Bryant--Salamon manifold of topology $S^3\times \mathbb{R}^4$. In particular, we describe new large families of complete $\mathbb{T}^2$-invariant associative submanifolds in them. |
| title | On $G_2$ manifolds with cohomogeneity two symmetry |
| topic | Differential Geometry 53C25, 53C29, 53C38, 53C40 |
| url | https://arxiv.org/abs/2306.03569 |