论文标题
每个点都包含一个大圆圈的表面形状
The shape of surfaces that contain a great and a small circle through each point
论文作者
论文摘要
我们对三维单元球体中表面的拓扑类型进行了分类，这些球体既包含一个大圆圈，又包含一个小圆圈。特别是，这些表面对五种正常形式之一是同构的，并且要么是单位四元组中圆的点乘积，要么是五个并发圆。我们对此类表面的真正单数基因座进行了分类，并表征了表面中的圆圈如何满足自我交流位点。
We classify the topological types of surfaces in the 3-dimensional unit sphere that contain both a great and a small circle through each point. In particular, these surfaces are homeomorphic to one of five normal forms and are either the pointwise product of circles in the unit quaternions or contain five concurrent circles. We classify the real singular loci of such surfaces and characterize how circles in the surface meet the self-intersection locus.
