论文标题
$ 3 $ sphere和$ 2 $ -sphere的凸polyhedra
Convex Polyhedra in the $3$-Sphere and Tilings of the $2$-Sphere
论文作者
论文摘要
我们表明，对于$ s^3 $中的每个凸多面体球$ p $，存在两个规范，非边缘到边缘的$ s^{2} $，其瓷砖的所有面都由$ p $的所有面和双convex polyhedral sphere $ p^*$ p^$ p $。根据$ s^{3} $的识别，与Lie Group $ su（2）$，以及$ s^{2} $的$ s^{2} $与单位球中的单位球$ su（2）$（2）$（2）$，我们的结果是通过考虑$ \\\\\\\\\\\\\\\ $ su（2）通过在$ su（2）$上使用左和右Maurer-Cartan表单来定义。
We show that for every convex polyhedral sphere $P$ in $S^3$, there exist two canonical, non-edge-to-edge tilings of $S^{2}$ whose tiles are given by all the faces of $P$ and the dual convex polyhedral sphere $P^*$ to $P$. Under the identifications of $S^{3}$ with the Lie group $SU(2)$, and of $S^{2}$ with the unit sphere in the Lie algebra $su(2)$ of $SU(2)$, our result is obtained by considering the set $\widetilde P$ of outward unit normal vectors to $P$ and the maps from $\widetilde P$ to $S^{2}$ defined by using the left and right Maurer-Cartan forms on $SU(2)$.
