标题： 按其奇点对Dupin环柄三次曲面的分类 显示英文标题

标题： Classification of Dupin Cyclidic Cubes by Their Singularities

摘要： 三重正交坐标系，其坐标线为圆或直线。 从技术上讲，它们由三线性有理四元数映射表示，并被称为Dupin环面立方体，自然地推广了Dupin环面主区域的双线性有理四元数参数化。 研究并分类了Dupin环面立方体及其在欧几里得空间中的奇点，直至Möbius等价性。 显示英文摘要

摘要： Triple orthogonal coordinate systems having coordinate lines as circles or straight lines are considered. Technically, they are represented by trilinear rational quaternionic maps and are called Dupin cyclidic cubes, naturally generalizing the bilinear rational quaternionic parametrizations of principal patches of Dupin cyclides. Dupin cyclidic cubes and their singularities are studied and classified up to M\"obius equivalency in Euclidean space.