Polars and antipodal sets for the outer $3$-symmetric space ${\mathbb{S}}^7\times {\mathbb{S}}^7$

Jost-Heinrich Eschenburg, Takashi Sakai

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…