Polars and antipodal sets for the outer $3$-symmetric space $\mathbb{S}^7 \times \mathbb{S}^7$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912574764744704 |
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| author | Eschenburg, Jost-Heinrich Sakai, Takashi |
| author_facet | Eschenburg, Jost-Heinrich Sakai, Takashi |
| contents | We determine the polar and the maximal antipodal set $P$ for the outer 3-symmetric space $\mathbb{S}^7 \times \mathbb{S}^7 = \mathrm{Spin}_8/G_2$ where the 3-symmetric structure is given by the triality automorphism $τ$ on $\mathrm{Spin}_8$. It turns out that $P$ has three elements. The 3-symmetric structure extends to a (non-abelian) $S_3$-structure which we also investigate. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_05912 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polars and antipodal sets for the outer $3$-symmetric space $\mathbb{S}^7 \times \mathbb{S}^7$ Eschenburg, Jost-Heinrich Sakai, Takashi Differential Geometry 53C30, 15A66 We determine the polar and the maximal antipodal set $P$ for the outer 3-symmetric space $\mathbb{S}^7 \times \mathbb{S}^7 = \mathrm{Spin}_8/G_2$ where the 3-symmetric structure is given by the triality automorphism $τ$ on $\mathrm{Spin}_8$. It turns out that $P$ has three elements. The 3-symmetric structure extends to a (non-abelian) $S_3$-structure which we also investigate. |
| title | Polars and antipodal sets for the outer $3$-symmetric space $\mathbb{S}^7 \times \mathbb{S}^7$ |
| topic | Differential Geometry 53C30, 15A66 |
| url | https://arxiv.org/abs/2509.05912 |