平移达布四次圆纹曲面与大达布四次圆纹曲面
Translational and great Darboux cyclides
AI总结：
本研究通过低次曲线模数值等价的组合学方法，对平移与大Darboux cyclides进行分类，推导得出不同空间中由圆构造的曲面上过一般点的圆数量结论。
摘要：
欧氏空间中由圆的逐点和构成的曲面，要么是共面的，要么过一般点的圆不超过2个。单位四元数中由圆的逐点积构成的曲面，过一般点的圆有2、3、4或5个。任意维数单位球面上过一般点含2个大圆的曲面，过一般点的圆有4、5、6个或无穷多个。这些是我们对平移与大Darboux cyclides（达布四次圆纹曲面）分类得到的部分推论。我们采用了与这类曲面上低次曲线集模数值等价相关的组合学方法。
英文摘要：
A surface that is the pointwise sum of circles in Euclidean space is either coplanar or contains no more than 2 circles through a general point. A surface that is the pointwise product of circles in the unit-quaternions contains either 2, 3, 4, or 5 circles through a general point. A surface in a unit-sphere of any dimension that contains 2 great circles through a general point contains either 4, 5, 6, or infinitely many circles through a general point. These are some corollaries from our classification of translational and great Darboux cyclides. We use the combinatorics associated to the set of low degree curves on such surfaces modulo numerical equivalence.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
