A Fueter operator for 3/2-spinors
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916601754812416 |
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| author | Sadegh, Ahmad Reza Haj Saeedi Nguyen, Minh Lam |
| author_facet | Sadegh, Ahmad Reza Haj Saeedi Nguyen, Minh Lam |
| contents | We show the non-compactness of moduli space of solutions of the monopole equations for $3/2$-spinors on a closed 3-manifold is equivalent to the existence of `3/2-Fueter sections' that are solutions of an overdetermined non-linear elliptic differential equation. These are sections of a fiber bundle whose fiber is a special 4-dimensional submanifold of the hyperkähler manifold of center-framed charged one $SU(2)$-instantons on $\mathbf{R}^4$. This fiber bundle does not inherit a hyperkähler structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12956 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Fueter operator for 3/2-spinors Sadegh, Ahmad Reza Haj Saeedi Nguyen, Minh Lam Differential Geometry Mathematical Physics Analysis of PDEs Geometric Topology 53Cxx, 57Rxx, 58Jxx, 57Kx We show the non-compactness of moduli space of solutions of the monopole equations for $3/2$-spinors on a closed 3-manifold is equivalent to the existence of `3/2-Fueter sections' that are solutions of an overdetermined non-linear elliptic differential equation. These are sections of a fiber bundle whose fiber is a special 4-dimensional submanifold of the hyperkähler manifold of center-framed charged one $SU(2)$-instantons on $\mathbf{R}^4$. This fiber bundle does not inherit a hyperkähler structure. |
| title | A Fueter operator for 3/2-spinors |
| topic | Differential Geometry Mathematical Physics Analysis of PDEs Geometric Topology 53Cxx, 57Rxx, 58Jxx, 57Kx |
| url | https://arxiv.org/abs/2405.12956 |