论文标题
Dupin Cyclidic Systems几何重新审视
Dupin cyclidic systems geometrically revisited
论文作者
论文摘要
Darboux提供了Dupin Cyclidic系统的诱导指标，即带有dupin cyclides和Spheres作为坐标表面的正交坐标系统。在这里，我们采取更加几何的观点，并讨论如何通过适当地演变出初始圆或杜宾辣椒来获得Dupin Cyclides和Lamé家族。这种方法表明，这些Lamé家族以各种空间形式的平行表面给出。
The induced metrics of Dupin cyclidic systems, that is, orthogonal coordinate systems with Dupin cyclides and spheres as coordinate surfaces, were provided by Darboux. Here we take a more geometric point of view and discuss how Dupin cyclides and Lamé families of Dupin cyclidic systems can be obtained by suitably evolving an initial circle or a Dupin cyclide, respectively. This approach reveals that those Lamé families are given by parallel surfaces in various space forms.
