New examples of $G_2$-instantons on $\mathbb{R}^4 \times S^3$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914930458886144 |
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| author | Alonso, Izar |
| author_facet | Alonso, Izar |
| contents | We study the existence of $\text{SU}(2)^2$-invariant $G_2$-instantons on $\mathbb{R}^4 \times S^3$ with the coclosed $G_2$-structures found on [arXiv:2209.02761]. We find an explicit 1-parameter family of $\text{SU}(2)^3$-invariant $G_2$-instantons on the trivial bundle on $\mathbb{R}^4 \times S^3$ and study its ''bubbling'' behaviour. We prove the existence a 1-parameter family on the identity bundle. We also provide existence results for locally defined $\text{SU}(2)^2$-invariant $G_2$-instantons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_08378 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | New examples of $G_2$-instantons on $\mathbb{R}^4 \times S^3$ Alonso, Izar Differential Geometry 53C07 We study the existence of $\text{SU}(2)^2$-invariant $G_2$-instantons on $\mathbb{R}^4 \times S^3$ with the coclosed $G_2$-structures found on [arXiv:2209.02761]. We find an explicit 1-parameter family of $\text{SU}(2)^3$-invariant $G_2$-instantons on the trivial bundle on $\mathbb{R}^4 \times S^3$ and study its ''bubbling'' behaviour. We prove the existence a 1-parameter family on the identity bundle. We also provide existence results for locally defined $\text{SU}(2)^2$-invariant $G_2$-instantons. |
| title | New examples of $G_2$-instantons on $\mathbb{R}^4 \times S^3$ |
| topic | Differential Geometry 53C07 |
| url | https://arxiv.org/abs/2311.08378 |