Hamiltonian dynamics and geometry on the two-plectic six-sphere
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914063341060096 |
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| author | Wagner, Maxime Wurzbacher, Tilmann |
| author_facet | Wagner, Maxime Wurzbacher, Tilmann |
| contents | We study the two-plectic geometry of the six-sphere induced by pulling back a canonical $G_2$-invariant three-form from $\mathbb{R}^7$ . Notably we explicitly prove non-flatness of this structure and show that its infinitesimal automorphisms are given by the exceptional Lie algebra $\mathfrak{g}_2$. Several interesting classes of solutions of the dynamical Hamilton-de Donder-Weyl equations with one- and two-dimensional sources are exhibited. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00756 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamiltonian dynamics and geometry on the two-plectic six-sphere Wagner, Maxime Wurzbacher, Tilmann Differential Geometry Mathematical Physics Symplectic Geometry 53C15, 53D05, 70G45, 70H05 We study the two-plectic geometry of the six-sphere induced by pulling back a canonical $G_2$-invariant three-form from $\mathbb{R}^7$ . Notably we explicitly prove non-flatness of this structure and show that its infinitesimal automorphisms are given by the exceptional Lie algebra $\mathfrak{g}_2$. Several interesting classes of solutions of the dynamical Hamilton-de Donder-Weyl equations with one- and two-dimensional sources are exhibited. |
| title | Hamiltonian dynamics and geometry on the two-plectic six-sphere |
| topic | Differential Geometry Mathematical Physics Symplectic Geometry 53C15, 53D05, 70G45, 70H05 |
| url | https://arxiv.org/abs/2502.00756 |